Answer :
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 [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 40, p =0.64[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 - 1.96\sqrt{\frac{0.64*0.36}{40}} = 0.4912[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 + 1.96\sqrt{\frac{0.64*0.36}{40}} = 0.7888[/tex]
The 95% confidence interval of the true proportion of men who enjoy watching sports more than movies is (0.4912, 0.7888).
Answer:
0.4913 < p < 0.7887
Step-by-step explanation:
See the attached picture for detailed answer.
