Chapter 10.1, Problem 5E

To determine

To check: the condition for confidence interval

Explanation of Solution

Given:

  $\begin{array}{l}{n}_1=\text{414}\\ x_1\text{=16}\\ n_2\text{=228}\\ x_2\text{=3}\end{array}$

Hypothesis test (3 condition)

Random: Not satisfied, because not arbitrary assigned.

Independent: cannot apply because of used all data values in the population and not used sample

Normal: Not satisfied, because there are only 3 successes in the second sample, which are not at least 10

Since the Random condition and Normal condition are not satisfied it is not fit to get a confidence interval for $p_1-p_2$ .