Question

When it comes to advertising, teens are not ready for the hard line messages that advertisers use in their ads. The Geppeto Group study found that 78% of teenagers enjoy ads that are silly in nature. Suppose that the study involved n=1030 teens. (a) Construct a 90% confidence interval for the proportion of teens who understand and enjoy ads that are silly in nature. Interpret the interval. (b) Using ONLY the interval constructed in (a), do you think the percentage of teenagers who enjoy silly ads differs from 75%? Test the hypothesis at the 10% level of significance. (c) Compute the p-value associated with this test.

Answer 1

The Geppeto Group has performed a study to check what proportion of teenagers enjoy silly ads. From the sample thry have obtained, 78% teenagers enjoy it. For testing we used proportion test at 10% los. The solution is provided in the images attached.
Given! t The 78% Geppeto shows that teenagers Group study enjoy siny = 1030 enjoy unagers silly ads. les @ = 0.78 m To test the null hypothesis 'Ho: P = Po us. ?HI:Pť po Test statistic is I za = 8-Po ---MOD At 90% c. I. zda = 1:645 - a). 90% c. II for Po is p - 1 To H test the null hypothesis, : P = 0.75 . vs. Hii pt 0.75 Po = 0.15, Qe = 1-0.75 = 0.25 At is 10 %. 90% Los c. the as confidence internal given above. Za

- DATE: 10.78:- 1.645. (0.75 x0.250.78 + 1-645 0.7580.25 V 1030 V 1030 = 10.7578, 0.8022) . I Po does not belong to above interval. Hence, we reject Ho at 10% 1.o.s. 1. The percentage of teenagers who enjoy silly ads is not 75%. ) p-value = p [z > Zcal 1 HoJ - under H₂ Zcal vn - 0.78 -0.75 10.75 x0.25 v 10 30 ... Z cam = 2.224 p-value = plz > 2.2241 tp-value = 0.013209 |