Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month (based on data from “Is Friday the 13th Bad for Your Health?” by Scanlon et al., British Medical Journal, Vol. 307, as listed in the Data and Story Line online resource of data sets). Construct a 95% confidence interval estimate of the mean of the population of differences between hospital admissions on days that are Friday the 6th of a month and days that are Friday the 13th of a month. 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.

Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal.