Question

Use the 4-step plan.

1. In a survey of 300 randomly selected Olympia students, participants were asked what their favorite and

least favorite subject was. The results were interesting. Math was picked more often for both categories. 93

picked math as their favorite subject and 126 picked math as their least favorite subject.

Construct and interpret a 95% confidence interval for the proportion of Olympia students who consider

math their favorite subject.

Answer 1

Answer: Here's the 4-step plan to construct and interpret a 95% confidence interval for the proportion of Olympia students who consider math their favorite subject:

Define the parameter of interest: Let p be the proportion of Olympia students who consider math their favorite subject.

Find the point estimate: The point estimate of p is the sample proportion of students who consider math their favorite subject, which is 93 / 300 = 0.31.

Find the standard error: The standard error of the point estimate is given by the formula:

SE = sqrt(p * (1 - p) / n), where n = 300 (the sample size).

Construct the confidence interval: A 95% confidence interval for p can be constructed using the point estimate and the standard error:

p ± 1.96 * SE.

The 95% confidence interval for p is: 0.31 ± 1.96 * SE = 0.31 ± 1.96 * sqrt(0.31 * 0.69 / 300) = (0.25, 0.37).

Interpretation: With 95% confidence, we estimate that the true proportion of Olympia students who consider math their favorite subject is between 0.25 and 0.37.