Surprisingly, injuries such as strains and sprains are higher among airport screeners than any other federal work group. A recent study found the injury rate for airport screeners was 29%, far exceeding the 4.5% injury rate for the rest of the federal workforce. Assume the sample sizes required to obtain these percentages were 75 and 125, respectively.
a. Determine if the sample sizes were large enough to allow the distribution of the difference of the sample proportions to be approximated with a normal distribution.
b. Conduct a hypothesis test to determine if the injury rate of airport screeners is more than 10% larger than that of the rest of the federal workforce. Use a significance level of 0.05.