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 1,080 viewers was selected and asked to watch the first two episodes. After viewing the episodes, 675 viewers indicated they would watch the new series. (Use t Distribution Table & z Distribution Table.) (Round your answers to 3 decimal places.)Required: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.
Question
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 1,080 viewers was selected and asked to watch the first two episodes. After viewing the episodes, 675 viewers indicated they would watch the new series. (Use t Distribution Table & z Distribution Table.) (Round your answers to 3 decimal places.)Required: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.
Solution
a. To estimate the value of the population proportion (p̂) of people who would watch the new series, we simply divide the number of viewers who indicated they would watch the series (675) by the total number of viewers sampled (1080).
So, p̂ = 675 / 1080 = 0.625
b. To develop a 99% confidence interval for the population proportion, we first need to find the standard error (SE) of the proportion. The formula for the standard error of a proportion is sqrt [ p̂(1 - p̂) / n ], where n is the sample size.
So, SE = sqrt [ 0.625(1 - 0.625) / 1080 ] = 0.014
Next, we need to find the z-score that corresponds to a 99% confidence level. From the z-distribution table, we find that the z-score is approximately 2.576.
Finally, we can calculate the confidence interval using the formula: p̂ ± Z * SE
Lower limit = 0.625 - 2.576 * 0.014 = 0.589 Upper limit = 0.625 + 2.576 * 0.014 = 0.661
So, the 99% confidence interval for the population proportion of people who would watch the new series is (0.589, 0.661).
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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 1,080 viewers was selected and asked to watch the first two episodes. After viewing the episodes, 675 viewers indicated they would watch the new series. (Use t Distribution Table & z Distribution Table.) (Round your answers to 3 decimal places.)Required: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.
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