Question

7) A random sample of 40 men were asked how if they enjoyed watching sports more than movies and 64% percent reported that they did. What is the 95% confidence interval of the true proportion of men who enjoy watching sports more than movies?

Answer 1

Answer:

The 95% confidence interval of the true proportion of men who enjoy watching sports more than movies is (0.4912, 0.7888).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$, and a confidence level of $1-\alpha$, we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$.

For this problem, we have that:

$n = 40, p =0.64$

95% confidence level

So $\alpha = 0.05$, z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$, so $Z = 1.96$.

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 - 1.96\sqrt{\frac{0.64*0.36}{40}} = 0.4912$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 + 1.96\sqrt{\frac{0.64*0.36}{40}} = 0.7888$

The 95% confidence interval of the true proportion of men who enjoy watching sports more than movies is (0.4912, 0.7888).

Answer 2

Answer:

0.4913 < p < 0.7887

Step-by-step explanation:

See the attached picture for detailed answer.