Several months ago while shopping, I was interviewed to see whether or not I'd be interested in signing up for a subscription to a yoga app. I fall into the
category of people who have a membership at a local gym, and guessed that, like me, many people in that category would not be interested in the app. My
friend Kala falls in the category of people who do not have a membership at a local gym, and I was thinking that she might like a subscription to the app. After
being interviewed, I looked at the interviewer's results. Of the 92 people in my market category who had been interviewed, 11 said they would buy a
subscription, and of the 105 people in Kala's market category, 28 said they would buy a subscription.
Assuming that these data came from independent, random samples, can we conclude, at the 0.05 level of significance, that the proportion $p_1$ of all mall
shoppers in my market category who would buy a subscription is less than the proportion $p_2$ of all mall shoppers in Kala's market category who would a
subscription?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consult a list of
formulas.)
(a) State the null hypothesis $H_0$ and the alternative hypothesis $H_1$.
$H_0$ :
$H_1$ :
(b) Determine the type of test statistic to use.
(Choose one)
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the $p$-value. (Round to three or more decimal places.)
