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 Carmen 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 81 people in my market category who had been interviewed, 18 said they would buy a subscription, and of the 117 people in Carmen's market category, 30 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, of all mall shoppers in my market category who would buy a subscription is less than the proportion p₂ of all mall shoppers in Carmen'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, and the alternative hypothesis H₁. Ho: P₁ P₂ H₁P₁ P2 (b) Determine the type of test statistic to use. Z (c) Find the value of the test statistic. (Round to three or more decimal places.) 0.498 u 1x a ロメロ S 00 Р =O OSO 20 OD