The times for untrained rats to run a standard maze has a N (65, 15) distribution where the times are measured in seconds. The researchers hope to show that training improves the times. The alternative hypothesis is
a. Ha: 碌 %26gt; 65.
b. Ha: %26gt; 65.
c. Ha: 碌 %26lt; 65.|||You want to improve the times, so we are looking or a smaller length of time for training. the alternate hypothesis is:
c. Ha: 碌 %26lt; 65.
== -- == -- ==
Consider the hypothesis as a trial against the null hypothesis. the data is evidence against the mean. you assume the mean is true and try to prove that it is not true. After finding the test statistic and p-value, if the p-value is less than or equal to the significance level of the test we reject the null and conclude the alternate hypothesis is true. If the p-value is greater than the significance level then we fail to reject the null hypothesis and conclude it is plausible. Note that we cannot conclude the null hypothesis is true, just that it is plausible.
If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be 渭 = d vs the alternate hypothesis 渭 鈮?d
if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.
if the null was 渭 鈮?100,000 vs the alternate 渭 %26lt; 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough.
if the null was 渭 鈮?100,000 vs. the alternate 渭 %26gt; 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result.
Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.|||c (we want the times to be faster ie less than 65seconds)|||a. Ha: 碌 %26gt; 65.
Thursday, December 15, 2011
Statistics: null hypothesis & alternative hypothesis?
I'm having trouble with understanding null %26amp; alternative hypothesis. Here is the question:
A poll of 1,068 adult Americans reveal that 48.0% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, test the claim that at least half of all voters prefer the Democrat.
A) Put the claim in symbolic form. Does the claim include equality?
B) State the null hypothesis and the alternative hypothesis.|||Null: p%26lt;.50, Alternate: p%26gt;.50 (this should be a "p is greater OR EQUAL to .5)
The claim is the alternate hypothesis. If it involves an inequality, the equal sign will always go with the alternate. In other words, once you figure out the equations, you will automatically know which one is the alternate, because it will have two signs (in this case, a 'greater than' sign and an 'equal' sign).
A poll of 1,068 adult Americans reveal that 48.0% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, test the claim that at least half of all voters prefer the Democrat.
A) Put the claim in symbolic form. Does the claim include equality?
B) State the null hypothesis and the alternative hypothesis.|||Null: p%26lt;.50, Alternate: p%26gt;.50 (this should be a "p is greater OR EQUAL to .5)
The claim is the alternate hypothesis. If it involves an inequality, the equal sign will always go with the alternate. In other words, once you figure out the equations, you will automatically know which one is the alternate, because it will have two signs (in this case, a 'greater than' sign and an 'equal' sign).
The alternative hypothesis?
The alternative hypothesis
A. Tells the value of the sample mean
B. None of these
C. Will always contain the equal sign
D. Is accepted if the null hypothesis is rejected|||D
[if] The null hypothesis is rejected IN FAVOUR of the alternative hypothesis
A. Tells the value of the sample mean
B. None of these
C. Will always contain the equal sign
D. Is accepted if the null hypothesis is rejected|||D
[if] The null hypothesis is rejected IN FAVOUR of the alternative hypothesis
Statistics-Null and Alternative hypothesis! HELP!!?
Generally it is assumed that female students have higher GPA鈥檚 than male students. Thus, I decided to test this common assumption. (Gender vs. GPA)
Using this information, can anyone please answer these quick questions:
State the hypothesis
Write out the null hypothesis
Write out the alternative hypothesis
THANKS YOU!!!|||State the hypothesis
female students have higher GPA鈥檚 than male students.
null hypothesis : No difference in GPA between males and females
alternative hypothesis : female students have higher GPA鈥檚 than male students
Using this information, can anyone please answer these quick questions:
State the hypothesis
Write out the null hypothesis
Write out the alternative hypothesis
THANKS YOU!!!|||State the hypothesis
female students have higher GPA鈥檚 than male students.
null hypothesis : No difference in GPA between males and females
alternative hypothesis : female students have higher GPA鈥檚 than male students
What hypothesis has been presented as an alternative to both the Hunting Hypothesis and the Gathering Hypothes?
It sounds like the question is saying that our ancestors survived by doing something other than hunting food and gathering food.
The only alternative to those would be foraging at the edge of large bodies of water, with limited fishing. I however would count both as types of gathering and hunting, respectively.
I have never heard of an alternative hypothesis to either method of food acquisition.|||Ranching and farming are the modern alternatives to hunting and gathering.
A few people still go bird or deer hunting, and we have those odd mushroom hunters, but for the most part we don't do it anymore.
Man is an animal. All animals are in a constant search for food. If they're tracking an animal, it's called hunting. If they see a blackberry along the way and eat it, it's called gathering. Eventually we realized that we could raise animals and food and not have to go looking for it.
The only alternative to those would be foraging at the edge of large bodies of water, with limited fishing. I however would count both as types of gathering and hunting, respectively.
I have never heard of an alternative hypothesis to either method of food acquisition.|||Ranching and farming are the modern alternatives to hunting and gathering.
A few people still go bird or deer hunting, and we have those odd mushroom hunters, but for the most part we don't do it anymore.
Man is an animal. All animals are in a constant search for food. If they're tracking an animal, it's called hunting. If they see a blackberry along the way and eat it, it's called gathering. Eventually we realized that we could raise animals and food and not have to go looking for it.
Is 'The probability of rolling a 3 with a dice is 1/6' a null hypothesis or an alternative hypothesis?
In theory, it is an alternative hypothesis, where to get any number on a die by rolling, it is 1 / 6.
In reality, the probability changes each time you roll, so it is a null hypothesis.|||It depends on what you want to show. If you want to show the die to be biased to have lower or higher probability of a 3 than 1/6, the assumption that it is fair will be the null hypothesis.
Generally, if you want to show that a certain theory holds, you make the inverse of the theory the null hypothesis, and show that, given the evidence, this is so unlikely that you have high confidence that your theory holds.|||It can be either.
If you want to test if the die is unbiased:
H0: prob of 3 = 1/6 --- null
H1: it is not 1/6 --- alternative
If you suspect that the die is biased and want to know that 3 has a probability of 2/3, then the following can be null and alternative hypotheses.
H0: prob of 3 = 2/3
H1: prob of 3 = 1/6
In reality, the probability changes each time you roll, so it is a null hypothesis.|||It depends on what you want to show. If you want to show the die to be biased to have lower or higher probability of a 3 than 1/6, the assumption that it is fair will be the null hypothesis.
Generally, if you want to show that a certain theory holds, you make the inverse of the theory the null hypothesis, and show that, given the evidence, this is so unlikely that you have high confidence that your theory holds.|||It can be either.
If you want to test if the die is unbiased:
H0: prob of 3 = 1/6 --- null
H1: it is not 1/6 --- alternative
If you suspect that the die is biased and want to know that 3 has a probability of 2/3, then the following can be null and alternative hypotheses.
H0: prob of 3 = 2/3
H1: prob of 3 = 1/6
Why are null and alternative hypothesis mutually exclusive?
They have to be by definition. One is the assumed hypothesis (null) and the other is an alternate (what is true if the null hypothesis isn't). By the very definition of the terms, they can't both be true. So H0: X= N goes with the alternatve H1: X IS NOT EQUAL to N.|||if they were'nt the experimental design would be impossible how can we have h0: there was no variance attributable to the treatment condition AND say hA: there is variance due to treatment condition AND have both be simultaneously true its like saying "the next sentence is true. The preceding sentence was false"
get my drift???
get my drift???
Can u give me any tip on deciding the null and alternative hypothesis in hypothesis testing?
Assuming that you are doing an experiment, the null hypothesis is that there will be no difference between the control and experimental data. The idea is to show that there is a significant difference (usually at the 95% level) between the two (alternative hypothesis), thereby disproving the null hypothesis. Remember that you can never prove anything in science, only disprove. The null hypothesis is the one you attempt to disprove.
What is an experimental/alternative hypothesis?
HELPPP ME|||It is the hypothesis you actually want to test.
For example, consider that you want to run an experiment with overweight and thin people to see who eats more potato chips.
Your null hypothesis would be "There is no difference in the amount of potato chips eaten by thin and overweight people".
Your experimental/alternative hypothesis would be "Overweight people consume MORE potato chips than thin people".
~Dr. B.~
For example, consider that you want to run an experiment with overweight and thin people to see who eats more potato chips.
Your null hypothesis would be "There is no difference in the amount of potato chips eaten by thin and overweight people".
Your experimental/alternative hypothesis would be "Overweight people consume MORE potato chips than thin people".
~Dr. B.~
Identify the null hypothesis,alternative hypothesis,test statistic,p-value,conclusion about the null hypothesi?
identify the null hypothesis,alternative hypothesis,test statistic,p-value,conclusion about the null hypothesis,and final conclusion that addresses the original claim.
According to a recent poll 52% of Americans would vote for the incumbent president.If a random sample of 250 people result in 45% who would vote for the incumbent, test the claim that the actual percentage is 52%.Use a 0.01 significance level
claim
test statistic
Critical Value
Comparison between test statistic and critical value
conclusion|||H0: proportion that would vote for the incumbent president =0.52
HA: proportion that would vote for the incumbent president %26lt; 0.52
Sample proportion phat = 0.45
Variance of proportion = p*(1-p)/n
= 0.52(0.48)/250 =0.0009984
S.D. of p is sqrt[0.000998] = 0.0316
Z = ( 0.45 - 0.52 ) / 0.0316 = -2.2154 --- test statistic
Critical value =-2.33
test statistic does not fall beyond the critical value
Conclusion: Do not reject H0;
52% of Americans would vote for the incumbent president.|||I believe the question is a difference in one bi proportion. the null is Ho: p=.5 and the alternative is H1: p%26gt;.5. Choose sig level of .01. Cr region is Reject null if z%26gt;z.05=1.645. test stat: Zcalc=x-n*Po/sq root of n*Po*Qo. Po=45% and Qo=55% osl or p value is Ho: p=.5 H1:p%26gt;.5 This should be enough info to solve
According to a recent poll 52% of Americans would vote for the incumbent president.If a random sample of 250 people result in 45% who would vote for the incumbent, test the claim that the actual percentage is 52%.Use a 0.01 significance level
claim
test statistic
Critical Value
Comparison between test statistic and critical value
conclusion|||H0: proportion that would vote for the incumbent president =0.52
HA: proportion that would vote for the incumbent president %26lt; 0.52
Sample proportion phat = 0.45
Variance of proportion = p*(1-p)/n
= 0.52(0.48)/250 =0.0009984
S.D. of p is sqrt[0.000998] = 0.0316
Z = ( 0.45 - 0.52 ) / 0.0316 = -2.2154 --- test statistic
Critical value =-2.33
test statistic does not fall beyond the critical value
Conclusion: Do not reject H0;
52% of Americans would vote for the incumbent president.|||I believe the question is a difference in one bi proportion. the null is Ho: p=.5 and the alternative is H1: p%26gt;.5. Choose sig level of .01. Cr region is Reject null if z%26gt;z.05=1.645. test stat: Zcalc=x-n*Po/sq root of n*Po*Qo. Po=45% and Qo=55% osl or p value is Ho: p=.5 H1:p%26gt;.5 This should be enough info to solve
Please simply the null and alternative hypothesis?
Consider the hypothesis as a trial against the null hypothesis. the data is evidence against the mean. you assume the mean is true and try to prove that it is not true.
If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be 渭 = d vs the alternate hypothesis 渭 鈮?d
if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.
if the null was 渭 鈮?100,000 vs the alternate 渭 %26lt; 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough.
if the null was 渭 鈮?100,000 vs. the alternate 渭 %26gt; 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result.
Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.|||The alternative hypothesis (or maintained hypothesis or research hypothesis) and the null hypothesis are the two rival hypotheses whose likelihoods are compared by a statistical hypothesis test. Usually the alternative hypothesis is the possibility that an observed effect is genuine and the null hypothesis is the rival possibility that it has resulted from random chance.
If your hypothesis was "Air helps people to live longer"
the null hypothesis would be "Air does not help people to live longer"
If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be 渭 = d vs the alternate hypothesis 渭 鈮?d
if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.
if the null was 渭 鈮?100,000 vs the alternate 渭 %26lt; 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough.
if the null was 渭 鈮?100,000 vs. the alternate 渭 %26gt; 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result.
Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.|||The alternative hypothesis (or maintained hypothesis or research hypothesis) and the null hypothesis are the two rival hypotheses whose likelihoods are compared by a statistical hypothesis test. Usually the alternative hypothesis is the possibility that an observed effect is genuine and the null hypothesis is the rival possibility that it has resulted from random chance.
If your hypothesis was "Air helps people to live longer"
the null hypothesis would be "Air does not help people to live longer"
What is an example of an alternative hypothesis?
it is an alternative reason why something might happen. eg finding a ten pound note puts you in a good mood for rest of the day. alternative hypothesis ; finding a ten pound note makes you more generous for rest of day.|||LOL! I love DB's answer! An alternative Hypothesis is a prediction that you make if you've used a non experimental method for your research, such as a survey, questionnaire or or observation. I.e. when you say that something is going to happen after carrying out one of the above methods. E.g. As DB said, students who use yahoo answers are less likely to complete homework independently. ;-)|||this is the alternative to the null hypothesis
e.g. The null hypothesis might be
There will be no possibilty of Kal- el doing his own psychology homework to day
The alternative hypothesis would be
There will be the possibility of Kal -el doing his own psychology homework today
Hypotheses are direct predictions of the expected outcome of your research and should be worded in the future tense and be specific
Incidentally I tutor one to one in Psych these days so send your cheque over|||Consider the hypothesis as a trial against the null hypothesis. the data is evidence against the mean. you assume the mean is true and try to prove that it is not true. After finding the test statistic and p-value, if the p-value is less than or equal to the significance level of the test we reject the null and conclude the alternate hypothesis is true. If the p-value is greater than the significance level then we fail to reject the null hypothesis and conclude it is plausible. Note that we cannot conclude the null hypothesis is true, just that it is plausible.
If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be 渭 = d vs the alternate hypothesis 渭 鈮?d
if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.
if the null was 渭 鈮?100,000 vs the alternate 渭 %26lt; 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough.
if the null was 渭 鈮?100,000 vs. the alternate 渭 %26gt; 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result.
Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.
e.g. The null hypothesis might be
There will be no possibilty of Kal- el doing his own psychology homework to day
The alternative hypothesis would be
There will be the possibility of Kal -el doing his own psychology homework today
Hypotheses are direct predictions of the expected outcome of your research and should be worded in the future tense and be specific
Incidentally I tutor one to one in Psych these days so send your cheque over|||Consider the hypothesis as a trial against the null hypothesis. the data is evidence against the mean. you assume the mean is true and try to prove that it is not true. After finding the test statistic and p-value, if the p-value is less than or equal to the significance level of the test we reject the null and conclude the alternate hypothesis is true. If the p-value is greater than the significance level then we fail to reject the null hypothesis and conclude it is plausible. Note that we cannot conclude the null hypothesis is true, just that it is plausible.
If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be 渭 = d vs the alternate hypothesis 渭 鈮?d
if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.
if the null was 渭 鈮?100,000 vs the alternate 渭 %26lt; 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough.
if the null was 渭 鈮?100,000 vs. the alternate 渭 %26gt; 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result.
Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.
Monday, December 12, 2011
Null and Alternative Hypothesis ?
I'm having trouble distinguishing between the null and alternative hypotheses in my online stats class.
Here's an example question: A store manager would like to know if the mean checkout time using the standard checkout method is longer than using the Fast Lane.
In the book they ask you to state the two hypotheses (null %26amp; alternative). Here's what the example showed:
H0: Us is less than or equal to Uf
H1: Us is greater than Uf
How do you decide which is null and which is alternative?|||The claim is always the alternative if it can assume more than one value. Here, the managaer wants to know (assume it is a claim).
Here's an example question: A store manager would like to know if the mean checkout time using the standard checkout method is longer than using the Fast Lane.
In the book they ask you to state the two hypotheses (null %26amp; alternative). Here's what the example showed:
H0: Us is less than or equal to Uf
H1: Us is greater than Uf
How do you decide which is null and which is alternative?|||The claim is always the alternative if it can assume more than one value. Here, the managaer wants to know (assume it is a claim).
An alternative hypothesis is a statement about a population parameter that is accepted if the null hypothesis?
is that english? woah! big words! lol
What is the null and alternative hypothesis?
college officials claim that the average freshman enrollment over the last 10 years is above the university's capacity of 6500 students|||null hypothesis= average freshman enrollment is within the university's capacity.
alternative hypothesis= average freshman enrollment is above the university's capacity.
alternative hypothesis= average freshman enrollment is above the university's capacity.
Statistics HELP- null and alternative hypothesis?
Nine students took the SAT. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Test the claim that the test preparation had no effect on their scores. Use 伪 = 0.05. Assume that the distribution is normally distributed.
What the null and alternative hypothesis be for this problem? It's confusing me.|||The null hypothesis in any experimental setting is going to be your prior expectation, in this case it is that "test preparation had no effect on their scores." In fact, our null hypothesis is almost always that our treatment had no effect. The alternative hypothesis is always that your null hypothesis is wrong, so in this case it is that test preparation did in fact have an effect on their scores.
What the null and alternative hypothesis be for this problem? It's confusing me.|||The null hypothesis in any experimental setting is going to be your prior expectation, in this case it is that "test preparation had no effect on their scores." In fact, our null hypothesis is almost always that our treatment had no effect. The alternative hypothesis is always that your null hypothesis is wrong, so in this case it is that test preparation did in fact have an effect on their scores.
Null hypothesis and Alternative Hypothesis?
A faculty member claims the amount of time spent by a student studying at home is not more than 2.25 hours.
With o as 0.75
A survey conducted to test the claim found 50 students studied 2.46 hours.
A significance level of 5 percent.
What is the null hypothesis what is the alternative hypothesis?
I'm so confused about this.|||Based on the way the question is written, the faculty says that the time spent is not more than 2.25 hrs. So, your null hypothesis would be that the average time spent is equal to 2.25 hours. Your alternative hypothesis would be that the average time spent is less than 2.25 hours.
When it comes to hypothesis, someone will make a claim that a certain event either less than, greater than, or not equal to the original number. Your null hypothesis will be a statement/equation that will read that the original number is true. Your alternate hypothesis will be rejecting the null hypothesis, whether it is in fact less than, greater than, or not equal to the original number.
Ex: I claim that the lifespan of a man is less than the US average of 75 years. Then, the null hypothesis would be that the US average is correct, or the US average is equal to 75 years. The alternate hypothesis, which will reject the null hypothesis, will translate to that the US average is less than 75 years.
Side note: I would be more inclined to believe that the faculty would claim that the amount of time spent is greater than 2.25, based on the survey results being greater than 2.25.
With o as 0.75
A survey conducted to test the claim found 50 students studied 2.46 hours.
A significance level of 5 percent.
What is the null hypothesis what is the alternative hypothesis?
I'm so confused about this.|||Based on the way the question is written, the faculty says that the time spent is not more than 2.25 hrs. So, your null hypothesis would be that the average time spent is equal to 2.25 hours. Your alternative hypothesis would be that the average time spent is less than 2.25 hours.
When it comes to hypothesis, someone will make a claim that a certain event either less than, greater than, or not equal to the original number. Your null hypothesis will be a statement/equation that will read that the original number is true. Your alternate hypothesis will be rejecting the null hypothesis, whether it is in fact less than, greater than, or not equal to the original number.
Ex: I claim that the lifespan of a man is less than the US average of 75 years. Then, the null hypothesis would be that the US average is correct, or the US average is equal to 75 years. The alternate hypothesis, which will reject the null hypothesis, will translate to that the US average is less than 75 years.
Side note: I would be more inclined to believe that the faculty would claim that the amount of time spent is greater than 2.25, based on the survey results being greater than 2.25.
. What is the difference between the null and alternative hypotheses statements in one-tailed and two-tailed t
What is the difference between the null and alternative hypotheses statements in one-tailed and two-tailed tests? How can manufacturing companies use the standard normal distribution to determine quality control of their products?
2. What is the "perfect" standard normal distribution? Explain your answer. What value is business research and hypothesis testing to a company?|||Consider the hypothesis as a trial against the null hypothesis. the data is evidence against the mean. you assume the mean is true and try to prove that it is not true.
If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be 渭 = d vs the alternate hypothesis 渭 鈮?d
if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.
if the null was 渭 鈮?100,000 vs the alternate 渭 %26lt; 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough.
if the null was 渭 鈮?100,000 vs. the alternate 渭 %26gt; 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result.
Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.
=== ===
You can use the standard normal in quality control because of the central limit theorem.
Let X1, X2, ... , Xn be a simple random sample from a population with mean 渭 and variance 蟽虏.
Let Xbar be the sample mean = 1/n * 鈭慩i
Let Sn be the sum of sample observations: Sn = 鈭慩i
then, if n is sufficiently large:
Xbar has the normal distribution with mean 渭 and variance 蟽虏 / n
Xbar ~ Normal(渭 , 蟽虏 / n)
Sn has the normal distribution with mean n渭 and variance n蟽虏
Sn ~ Normal(n渭 , n蟽虏)
The great thing is that it does not matter what the under lying distribution is, the central limit theorem holds. It was proven by Markov using continuing fractions.
if the sample comes from a uniform distribution the sufficient sample size is as small as 12
if the sample comes from an exponential distribution the sufficient sample size could be several hundred to several thousand.
if the data comes from a normal distribution to start with then any sample size is sufficient.
for n %26lt; 30, if the sample is from a normal distribution we use the Student t statistic to estimate the distribution. We do this because the Student t takes into account the uncertainty in the estimate for the standard deviation.
if we now the population standard deviation then we can use the z statistic from the beginning.
the value of 30 was empirically defined because at around that sample size, the quantiles of the student t are very close the quantiles of the standard normal.
=== ===
The perfect standard normal is Normal(渭 = 0, 蟽虏 = 1).
as n 鈫?鈭? Xbar ~ Normal(渭x , 蟽x虏 / n)
and
(Xbar - 渭x ) / sqrt( 蟽x虏 / n) ~ Normal(渭 = 0, 蟽虏 = 1)
because of this, in a sample of sufficient size we can approximate the behavior of the mean with the normal distribution which is easily translated into the standard normal. This is the basis for nearlly all parametric hypothesis testing.
2. What is the "perfect" standard normal distribution? Explain your answer. What value is business research and hypothesis testing to a company?|||Consider the hypothesis as a trial against the null hypothesis. the data is evidence against the mean. you assume the mean is true and try to prove that it is not true.
If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be 渭 = d vs the alternate hypothesis 渭 鈮?d
if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.
if the null was 渭 鈮?100,000 vs the alternate 渭 %26lt; 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough.
if the null was 渭 鈮?100,000 vs. the alternate 渭 %26gt; 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result.
Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.
=== ===
You can use the standard normal in quality control because of the central limit theorem.
Let X1, X2, ... , Xn be a simple random sample from a population with mean 渭 and variance 蟽虏.
Let Xbar be the sample mean = 1/n * 鈭慩i
Let Sn be the sum of sample observations: Sn = 鈭慩i
then, if n is sufficiently large:
Xbar has the normal distribution with mean 渭 and variance 蟽虏 / n
Xbar ~ Normal(渭 , 蟽虏 / n)
Sn has the normal distribution with mean n渭 and variance n蟽虏
Sn ~ Normal(n渭 , n蟽虏)
The great thing is that it does not matter what the under lying distribution is, the central limit theorem holds. It was proven by Markov using continuing fractions.
if the sample comes from a uniform distribution the sufficient sample size is as small as 12
if the sample comes from an exponential distribution the sufficient sample size could be several hundred to several thousand.
if the data comes from a normal distribution to start with then any sample size is sufficient.
for n %26lt; 30, if the sample is from a normal distribution we use the Student t statistic to estimate the distribution. We do this because the Student t takes into account the uncertainty in the estimate for the standard deviation.
if we now the population standard deviation then we can use the z statistic from the beginning.
the value of 30 was empirically defined because at around that sample size, the quantiles of the student t are very close the quantiles of the standard normal.
=== ===
The perfect standard normal is Normal(渭 = 0, 蟽虏 = 1).
as n 鈫?鈭? Xbar ~ Normal(渭x , 蟽x虏 / n)
and
(Xbar - 渭x ) / sqrt( 蟽x虏 / n) ~ Normal(渭 = 0, 蟽虏 = 1)
because of this, in a sample of sufficient size we can approximate the behavior of the mean with the normal distribution which is easily translated into the standard normal. This is the basis for nearlly all parametric hypothesis testing.
Simple statistics question on alternative hypothesis?
A dose of the drug Captopril, designed to LOWER systolic blood pressure, is administered to 10 randomly selected volunteers, and the SBP is measured before and after the pill.
渭B = mean SBP before pill
渭A = after pill
What is the alternative hypothesis?
A. H1: 渭B = 渭A
B. H1: 渭B 鈮?渭A
C. H1: 渭B 鈮?渭A
D. H1: 渭B %26gt; 渭A
thanks in advance to whoever helps out..|||The answer is D. Since the pill is designed to lower the SBP, we want to know if mean SBP is lower after the pill.
What about the other answers? Answer A is not correct, because the equality is the *null* hypothesis. B is incorrect, because it is the alternative hypothesis for a *two-tailed test*. If we just wanted to know if the pill *changed* SBP, without specifying whether the change is up or down, then B would be correct. Because C has a weak inequality (greater than or equal sign), it is neither a null hypothesis nor an alternative hypothesis.
Hope this helps.|||D.
渭B = mean SBP before pill
渭A = after pill
What is the alternative hypothesis?
A. H1: 渭B = 渭A
B. H1: 渭B 鈮?渭A
C. H1: 渭B 鈮?渭A
D. H1: 渭B %26gt; 渭A
thanks in advance to whoever helps out..|||The answer is D. Since the pill is designed to lower the SBP, we want to know if mean SBP is lower after the pill.
What about the other answers? Answer A is not correct, because the equality is the *null* hypothesis. B is incorrect, because it is the alternative hypothesis for a *two-tailed test*. If we just wanted to know if the pill *changed* SBP, without specifying whether the change is up or down, then B would be correct. Because C has a weak inequality (greater than or equal sign), it is neither a null hypothesis nor an alternative hypothesis.
Hope this helps.|||D.
Whats the type 1 error when given null and alternative hypothesis?
rejecting the null hypothesis when it is in fact true is a type 1 error
accepting the null hypothesis when it is wrong is type 2 error
accepting the null hypothesis when it is wrong is type 2 error
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