What is a Null and alternative hypothesis?

the question says....a manager believes that the average of a product is $75. A sample of 36 is taken. The average price is 72.50. The population variance is 144.





what is the null and alternative, using a critical value and P value, test the hypothesis at the 5% level of signifigance.





I thought you cant use both a critical value or p-value, its either or, right?|||ANSWER: Conclusion: Null Hypothesis H0: 渭 = 渭0 (Null Hypothesis) is true with 95% confidence.





Why??


SINGLE SAMPLE TEST, TWO-TAILED, 6 - Step Procedure for t Distributions, "two-tailed test"





Step 1: State the hypothesis to be tested.


Null Hypothesis H0: 渭 = 渭0


Alternate Hypothesis H1: 渭 鈮?渭0








Step 2: Determine a planning value for 伪 [level of significance] =


0.05


Step 3: From the sample data determine x-bar, s and n; then compute


Standardized Test Statistic: t = ( x-bar - 渭0 )/( s/ SQRT(n) )





x-bar: Est. of the Pop. Mean (statistical mean of the sample) =


72.5


n: number of individuals in the sample =


36


s: sample standard deviation =


24 [144/sqrt(36)]








渭0: Population Mean =


75


significant digits =


3


Standardized Test Statistic t = ( 72.5 - 75 )/( 24 / SQRT( 36 )) =


0.625





Step 4: Using Students t distribution, 'lookup' the area outside of t = TDIST( 0.625 , 35 , 2 ) using Excel TDIST(x, n-1 degrees_freedom, 2 tails)


using Excel TDIST(x, n-1 degrees_freedom, 2 tails)








Step 5: Area in Step 4 is equal to P value =


0.536


based on n -1 = 35 df (degrees of freedom).





Table look-up value shows area under the 35 df curve outside of t = +/- 0.625 is (approx.)


P value = 0.536 [2 * 0.268] by addition of both 'tails' of t distribution.





Step 6: For P 鈮?伪, fail to reject H0; and for P %26lt; 伪, reject H0 with


0.95% confidence in the conclusion.





Conclusion: Null Hypothesis H0: 渭 = 渭0 (Null Hypothesis) is true with 95% confidence.





Note: level of significance [伪] is the maximum level of risk an experimenter is willing


to take in making a "reject H0" or "conclude H1" conclusion (i.e. it is the maximum


risk in making a Type I error).