Question

Confidence Intervals: Generate the specified confidence interval. In a survey of 700 community community college students, 481 indicated that they have read a book for personal enjoyment during the school year. Determine the 95% confidence interval for the proportion of community college students who have read a book for personal enjoyment during the school year.

Answer 1

The 95% confidence interval for the proportion of community college students who have read a book for personal enjoyment during the school year is approximately (0.663,0.749).

To determine the 95% confidence interval for the proportion of community college students who have read a book for personal enjoyment during the school year, we can use the formula for a confidence interval for a proportion. The sample proportion (p^​) is calculated as the ratio of the number of students who have indicated reading a book (481) to the total sample size (700). The standard error of the proportion (SE( p^​)) is computed as
`√(p^(1-p^/n)`, where n is the sample size.

Substituting the values into the formula for the confidence interval, we get:

Confidence Interval= p^​±Z×SE( p^​)

For a 95% confidence interval, the critical z-value is approximately 1.96. Substituting the values, we find that the 95% confidence interval for the proportion of community college students who have read a book for personal enjoyment during the school year is approximately (0.663,0.749). This means that we are 95% confident that the true proportion of students who have read a book falls within this interval.