SOLUTION: #9-6
Netflix is considering a new romcom (romantic comedy) series. Before making a final decision, the producers design an experiment to estimate the proportion of viewers who w
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-> SOLUTION: #9-6
Netflix is considering a new romcom (romantic comedy) series. Before making a final decision, the producers design an experiment to estimate the proportion of viewers who w
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Question 1202887: #9-6
Netflix is considering a new romcom (romantic comedy) series. Before making a final decision, the producers design an experiment to estimate the proportion of viewers who would watch the series. A random sample of 560 viewers was selected and asked to watch the first two episodes. After viewing the episodes, 350 viewers indicated they would watch the new series. (Round your answers to 3 decimal places.)
a. Estimate the value of the population proportion of people who would watch the new series.
b. Develop a 99% confidence interval for the population proportion of people who would watch the new series. ____ and ____.
b. Develop a 99% confidence interval for the population proportion of people who would watch the new series. ____ and ____.
critical z-score for 95% confidence interval is plus or minus z = 1.95996.
z-score formula on the high end of the confidence interval becomes:
1.95996 - (x-.625) / s
(x-m) is the margin of error, where m would be equal to .625 which is the mean value of the proportion of viewers who would watch the series and x is the value of the high end of the confidence interval.
s is the standard error, which is equal to sqrt(.625 * (1 - .625) / 560) = .0204579.
z-score formula becomes 1.95996 = (x - .625) / .0204579.
solve for x to get x = 1.95996 * .0204579 + .625 = .665097.
z-score formula on the low end of the confidence interval becomes -1.95996 *.0204579 + .625 = .584903.
your 95% confidence interval is from .584903 to .665097.
this is what it looks like on a graph.
