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 1,040 viewers was selected and asked to watch the first two episodes. After viewing the episodes, 650 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.

Answer 1

Using the z-distribution, as we are working with a proportion, it is found that:

a) The population proportion is of 0.625.

b) The interval is (0.586, 0.664).

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

• $\pi$ is the sample proportion.

• z is the critical value.

• n is the sample size.

In this problem, we have a 99% confidence level, hence$\alpha = 0.99$, z is the value of Z that has a p-value of $\frac{1+0.99}{2} = 0.995$, so the critical value is z = 2.575.

The sample size and the population proportion are given, respectively, by:

$n = 1040, \pi = \frac{650}{1040} = 0.625$

Hence, the bounds of the interval are given by:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.625 - 2.575\sqrt{\frac{0.625(0.375)}{1040}} = 0.586$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.625 + 2.575\sqrt{\frac{0.625(0.375)}{1040}} = 0.664$

More can be learned about the z-distribution at brainly.com/question/25890103