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.Fridaythe 6th.Fridaythe 13th.1014713111411103614Construct a 95% confidence interval estimate of the mean of the population of differences between hospital admissionson days that are Friday the 6th of a month and days that are Fridays 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.

The formulas used are Mean: d¯=∑din Standard deviation: sd=1n-1∑di-d¯2 95% confidence interval: d¯±tc×sdnLet d be the difference between Friday on the 6th of a month and Friday on the 13th of the same month. d=10-14, 7-13, 11-14, 11-10, 3-5, 6-14 d=-4, -6, -3, 1, -2, -8 Now mean: d¯=∑din =-4+-6+-3+1+-2+-86 =-226 =-3.6667 and standard deviation: sd=1n-1∑di-d¯2 =16-1-4--3.66672+-6--3.66672+........+-8--3.66672 =9.86666667 =3.1411 Now, at a 95% confidence interval α=1-0.95 =0.05 then α2=0.025 degrees of freedom df=n-1 =6-1 =5 and critical value tc=t0.025 =2.571 using excel =T.INV(1-0.025,5) hence 95% confidence interval: d¯±tc×sdn ⇒ 3.6667±2.571×3.14116 ⇒ 3.6667±3.2969 ⇒ -6.9636,-0.3698 Therefore, the 95% confidence interval is -6.9636≤μd≤-0.3698 Hence, as the confidence interval does not contain 0, we can conclude that the 13th day of a month falls on a Friday, so the number of hospital admissions from motor vehicle crashes is not affected.