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. *find t statistic, critical value, and hypothesis.

Friday_the_6th   Friday_the_13th
10   11
9   10
2   12
10   10
5   12

Answer 1

Let d =  Friday_the_6th - Friday_the_13th

Following table shows the calculations for differences and standard deviation of differences:

Friday the 6th	Friday the 13th	d	(d-mean)^2
10	11	-1	7.84
9	10	-1	7.84
2	12	-10	38.44
10	10	0	14.44
5	12	-7	10.24
Total		-19	78.8

Since confidence interval contains zero so there is no evidence that when the 13th day of a month falls on a​ Friday, the numbers of hospital admissions from motor vehicle crashes are not affected.

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Following is the two tailed test:

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