Large companies typically collect volumes of data before designing a product, not only to gain information as to whether the product should be released, but also to pinpoint which markets would be the best targets for the product. Several months ago, I was interviewed by such a company while shopping at a mall. I was asked about my exercise habits and whether or not I'd be interested in buying a video/DVD designed to teach stretching exercises. I fall into the male, 18 – 35-years-old category, and I guessed that, like me, many males in that category would not be interested in a stretching video. My friend Amanda falls in the female, older-than-35 category, and I was thinking that she might like the stretching video. After being interviewed, I looked at the interviewer's results. Of the 97 people in my market category who had been interviewed, 16 said they would buy the product, and of the 101 people in Amanda's market category, 31 said they would buy it. Assuming that these data came from independent, random samples, can we conclude (at the 0.05 level of significance) that the proportion p1 of all mall shoppers in my market category who would buy the product is less than the proportion p2 of all mall shoppers in Amanda's market category who would buy the product? 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. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the value of the test statistic. (Round to three or more decimal places.) c. Find the critical value at the 0.05 level of significance. Round to three or more decimal places. d. Can we conclude that the proportion of mall shoppers in my market category who would buy the product is less than the proportion in Amanda's market category who would?
Large companies typically collect volumes of data before designing a product, not only to gain information as to whether the product should be released, but also to pinpoint which markets would be the best targets for the product. Several months ago, I was interviewed by such a company while shopping at a mall. I was asked about my exercise habits and whether or not I'd be interested in buying a video/DVD designed to teach stretching exercises. I fall into the male, 18 – 35-years-old category, and I guessed that, like me, many males in that category would not be interested in a stretching video. My friend Amanda falls in the female, older-than-35 category, and I was thinking that she might like the stretching video. After being interviewed, I looked at the interviewer's results. Of the 97 people in my market category who had been interviewed, 16 said they would buy the product, and of the 101 people in Amanda's market category, 31 said they would buy it. Assuming that these data came from independent, random samples, can we conclude (at the 0.05 level of significance) that the proportion p1 of all mall shoppers in my market category who would buy the product is less than the proportion p2 of all mall shoppers in Amanda's market category who would buy the product? 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.
a. State the null hypothesis H0 and the alternative hypothesis H1.
b. Find the value of the test statistic. (Round to three or more decimal places.)
c. Find the critical value at the 0.05 level of significance. Round to three or more decimal places.
d. Can we conclude that the proportion of mall shoppers in my market category who would buy the product is less than the proportion in Amanda's market category who would?
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