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alexandr402 [8]
3 years ago
13

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?

Mathematics
2 answers:
stepladder [879]3 years ago
8 0

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).

soldi70 [24.7K]3 years ago
8 0

Answer:

0.4913 < p < 0.7887

Step-by-step explanation:

See the attached picture for detailed answer.

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