Can someone help me out with a null and alternative hypothesis problem?

Magazine polled 500 13-year-olds online to get a glimpse into their world. 13-year-olds in 2005 enjoy their relationships with their parents, are less likely to drink or do drugs than previous generations, and they are highly focused, competitive and determined to succeed. The overscheduled toddlers of the 1990s are now controlling their own schedules, and in many cases, their days are just as jam-packed as ever. It seems today's teens are not only used to being extremely busy, they thrive on it. One result from time poll was that 53% of the 13 year olds polled said their parents are very involved in their lives. Suppose that 200 of the 13-year-olds were boys and 300 of them were girls. We wish to find out if the proportion of 13-year-old boys and girls who say that their parents are very involved in their lives are the same.


a) Using symbols, state appropriate null and alternative hypothesis to test the proportions for 13-year-old boys versus 13-yr-old girls.|||In your notation for A=boys and B=girls, the hypotheses should actually be





H0: p A=p B and


HA: p A 鈮?p B.





I'm assuming this is for an intro stats class so the null hypotheses should ALWAYS have the equality statement and the alternative hypothesis should NEVER have an equality statement. Also, your hypotheses statements are for the population parameters so it should be p, not p-hat. p-hat is notation for the sample statistic.





What the previous answer said about type I and II error is not true, one type is not always worst than the other. It is situationally dependent.|||Step 1: determine what it is you're trying to show.


let's assign B = boys who say parents are involved in their lives, and G = girls who say the same. You are trying to show that B = G using the data, correct?





Step 2: construct the null. Assume that B and G are not equal.


Ho : B != G, that is your null. It's the "catch-all" that basically means "hey, the alternative does not hold water."





Step 3: construct the alternative.


Ha : B = G. This is your alternative, the case where boys and girls say they have involved parents equally.





In hypothesis testing, the thing we MUST stay away from is falsely saying that claim is true. This is also known as type I error, and is much more serious than type II error, which is showing that the alternative hypothesis is false.


Hence, we speak in terms of "rejecting the null" or "not rejecting the null", not in terms of the alternative. This helps us keep away from the mindset of manipulating data and using circumstantial evidence in efforts of "proving" a hypothesis.





P.S. you are correct in your usage of P. I left it out since I'm usually too lazy to write it, but just be careful how you define your variables. As for the hat, many use it to indicate exogenous variables (values derived from data outside the system, basically values that you didn't get from calculation), but again it's not always needed unless your professor strictly enforces such notation.