Question

In: Statistics and Probability

We would like to know: "What percentage of college students drink alcohol every day?" In a...

We would like to know: "What percentage of college students drink alcohol every day?" In a random sample of 500 students, 75 said they drink alcohol every day. Use the data to construct a 95% confidence interval to answer to the question. You MUST show your work to receive full credit.

Solutions

Expert Solution

Solution :

Given that,

n = 500

x = 75

Point estimate = sample proportion = = x / n = 0.15

1 - = 0.85

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.15 * 0.85) / 500)

= 0.031

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.15 - 0.031 < p < 0.15 + 0.031

0.119 < p < 0.181

( 0.119 , 0.181 )

orchestra answered 1 year ago
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