In a random sample of 400 radio reviewers, 300 felt that radiostation policy of

Question

In a random sample of 400 radio reviewers, 300 felt that radiostation policy of running three consecutive commercials followed bya station break and two more commercials (i.e. five commercials intotal) in less than three minutes was extremely poor policy andgave the appearance of "cluttering" the air with commercials.

a. At the 1% level of significance, is this findingconsistent with a claim that two-thirds of the listeners in thepopulation sampled feel that this is an extremely poor policy?

b. Find the confidence interval for this data using (a)calculations, and (b) charts.

Explanation / Answer

phat=300/400= 0.75 p=2/3=0.67 =0.01, Z(0.005)=2.58 (a) The test hypothesis is Ho: p = 0.67 Ha: p not equal 0.67 The test statistics is Z=(phat - p) / p*(1-p)/n = (0.75 -0.67) / sqrt(0.67 * (1-0.67)/400) = 3.4 Since Z=3.4>2.58, reject Ho. (b) The 99% CI is phat±Z*p*(1-p)/n --> 0.75 ± 2.58 *sqrt(0.67*(1-0.67)/400) --> (0.6893, 0.8107)

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