Data on the numbers of hospital admissions resulting from motor vehicle crashes

Question

Data on the numbers of hospital admissions resulting from motor vehicle crashes are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the mean of the population of differences between hospital admissions. Use the confidence interval to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected. In this example, mu d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the number of hospital admissions on Friday the 6th minus the number of hospital admissions on Friday the 13th. Find the 95% confidence interval.

Explanation / Answer

difference (d) -2......-7 .......-9........-1 .......-4

mean = (-2 -7 -9 -1 -4)/5 = -4.6

sum(d^2) = 4 + 49 + 81 + 1 + 16 = 151

variance = 151/5 - 4.6^2 = 9.04

standard deviation = sqrt(variance) = 3.01

confidence interval = mean +/- z * std/sqrt(n)

lower limit = -4.6 - 1.96 * 3.01/sqrt(5) = -7.24

upper limit = -4.6 + 1.96 * 3.01/sqrt(5) = -1.96

confidence interval is

-7.24 < ud < -1.97

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