Question

An archaeologist discovers only seven fossil skeletons from a previously unknown species of horse. Reconstructions of the skeletons of these seven horses show the shoulder heights (in centimeters) to be:

132 141 143 107 123 145 163

Find a 95% confidence interval for the mean shoulder height. Show work.

Answer 1

solution:

first of all we have to calculate the mean and standard deviation of the sample data

mean =

SD = S =

sample size = n = 7

sample mean = = 136.29

sample standard deviatio = S = 17.84

confidence interval (CL) = 95% = 0.95

significance level () = 1 - CL = 1 - 0.95 = 0.05

degree of freedom = df = n - 1 = 7 - 1 = 6

since population standard deviation is unknown and sample size is also small , so we will use the t distribution to find the confidence interval

critical value of

confidence interval of mean =

lower limit of confidence interval = 136.29 - 16.5 = 119.79

upper limit of confidence interval = 136.29 + 16.5 = 152.79

confidence iterval for the mean shouler height is (119.79 , 152.79)

demonstration of the value of t from the ta table