Question

Specimen 1 2 3 4 5 6 7 8 9

Steel ball 50 57 61 71 68 54 65 51 53

Diamond 52 55 63 74 69 56 68 51 56

Construct a​ 95% confidence interval to judge whether the two indenters result in different​ measurements, where the differences are computed as​ 'diamond minus steel​ ball'.

Answer 1

Solution:

Confidence interval for difference between two population means of paired samples is given as below:

Confidence interval = Dbar ± t*SD/sqrt(n)

From given data, we have

Dbar = 1.555555556

SD = 1.666666667

n = 9

df = n – 1 = 8

Confidence level = 95%

Critical t value = 2.3060

(by using t-table)

Confidence interval = Dbar ± t*SD/sqrt(n)

Confidence interval = 1.555555556 ± 2.3060*1.666666667/sqrt(9)

Confidence interval = 1.555555556 ± 1.2811

Lower limit = 1.555555556 - 1.2811 = 0.27

Upper limit = 1.555555556 + 1.2811 = 2.84

Confidence interval = (0.27, 2.84)

The two indenters results in different measurements because above interval does not include zero.