Question

A recent survey collected information on television viewing habits from a random sample of 1,000 people in the united states. Of those sampled, 37 percent indicated that their favorite sport to watch on television was american football. (a) construct and interpret a 95 percent confidence interval for the proportion of all people in the united states who would indicate that their favorite sport to watch on television is american football.

Answer 1

The confidence interval and the interpretation of it is; CI = (0.34, 0.40) which means that the 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).

What is the confidence interval?

We are given;

Sample proportion; p = 37% = 0.37

Sample size; n = 1000

The confidence interval for the population proportion, is given by the formula;

CI = p ± z√[(p(1 - p)/n)]

z for Confidence level of 95% is z = 1.96.

Thus;

CI = 0.37 ± 1.96√[(0.37(1 - 0.37)/1000)]

CI = 0.37 ± 0.03

CI = (0.34, 0.40)

Thus, the 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).

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