Question

Listed below are the heights of candidates who won elections and the heights of the candidates with the next highest number of votes. The data are in chronological​ order, so the corresponding heights from the two lists are matched. Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Construct a​ 95% confidence interval estimate of the mean of the population of all​ "winner/runner-up" differences. Does height appear to be an important factor in winning an​ election?

Winner 69 73 77 72 76 78 74 78

​Runner-Up 71 68 73 69 72 73 73 73

Construct the​ 95% confidence interval.​ (Subtract the height of the​ runner-up from the height of the winner to find the​ difference, d.)

Answer 1

Confidence interval formula for paired t test.

Sample size = 8

Degree of freedom =n-1 = 8-1 = 7

t critical value is =2.365..................by using t table or by using Excel command =TINV(0.05,7)

Substitute all known values into confidence interval formula now,

=>(1.06,5.19)

Therefore, 95% confidence interval is