Chapter 10.1, Problem 12E

To determine

To find: The 95% confidence interval for the differences in the proportion of white and young people who listen rap daily.

Answer to Problem 12E

The confidence interval is (0.1959, 0.3641)

Explanation of Solution

Given:

  $x_1=368,n_1=634,x_2=130,n_2=567$

Formula used:

The formula to compute the confidence interval for difference in population proportions is:

  $CI=\left({\widehat{p}}_1-{\widehat{p}}_2\right)\pm z_{\alpha /2}\times \sqrt{\frac{{\widehat{p}}_1\left(1-{\widehat{p}}_1\right)}{n_1}+\frac{{\widehat{p}}_2\left(1-{\widehat{p}}_2\right)}{n_2}}$

Calculation:

The 95% confidence interval using Ti-83 plus calculator is computed as:

  

Thus, the confidence interval is (0.299, 0.403)

Interpretation:

Thus, it could be interpreted that there is 90% probability that the difference in the proportion of young people that listen rap daily lies between 0.299 and 0.403.