Television networks rely heavily on ratings of television shows when deciding whether to renew a show for another season. Suppose the Hyena network has decided that "Miniature Golf with the Stars" will only be renewed if it can be established that more than 12% of people in a nationwide poll watch the show. Let p be the true proportion of people in the country who watch the show. A random sample of 2500 US adults was taken and 275 said they watched the show. Construct a 90% interval for the true proportion of US adults who watch the show. a. Which interval should you use and what are the conditions? b. Calculate the interval. c. Interpret the interval.
Added by Patricia E.
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We should use a confidence interval for a proportion since we are dealing with a proportion (p) of people who watch the show. The conditions for constructing a confidence interval for a proportion are: Show more…
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TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streaming is gaining in popularity. A poll reported that 52% of 2342 American adults surveyed said they have watched digitally streamed TV programming on some type of device. (a) Calculate and interpret a confidence interval at the 99% confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time. (Round your answers to three decimal places.) (0.493, 0.547) Interpret the resulting interval. We are 99% confident that this interval contains the true population proportion. We are 99% confident that the true population proportion lies below this interval. We are 99% confident that this interval does not contain the true population proportion. We are 99% confident that the true population proportion lies above this interval. (b) What sample size would be required for the width of a 99% CI to be at most 0.06 irrespective of the value of p̂? (Round your answer up to the nearest integer.) 7361 You may need to use the appropriate table in the Appendix of Tables to answer this question.
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