The new health care plan that the federal government recently implemented has caused people to become concerned that a shortage of primary care physicians, particularly in underserved rural areas, will occur. Random samples of patient visits to primary care physicians in both rural and urban areas were selected. The number of days the patients had to wait for an appointment was recorded. The summarized data for each sample are shown in the following table:

a. Perform a hypothesis test using α = 0.01 to determine if the average number of days patients in urban areas waited to see their primary care physicians differs from the average number of days patients in rural areas waited.

b. Determine the p value and interpret the results.

c. Construct a 99% confidence interval to estimate the difference in the average number of days patients in urban areas waited to see their primary care physicians vs. the average number of days patients in rural areas waited.

d. Verify your results using PHStat.

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Sample mean Sample size Population standard deviation Rural 11.7 32 5.0 Urban 8.6 30 3.5