Question

TestScore

53 53 56 56 56 58 58 58 59 59 59 60 60 62 63 63 63 64 65 65 66 67 67 67 67 68 69 69 69 69 71 71 72 72 72 72 73 73 73 73 73 74 75 75 75 76 76 76 76 77 77 77 77 77 78 78 78 79 79 79 79 80 80 80 80 80 80 81 81 81 82 82 83 83 83 83 84 84 84 84 84 85 85 85 85 86 86 87 87 87 87 87 88 88 89 89 89 90 90 90 90 91 93 96

Determine the 95% confidence interval of this data.

Answer 1

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 75.67307692

S = 10.32053501

n = 104

df = n – 1 = 103

Confidence level = 95%

Critical t value = 1.9833

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 75.67307692 ± 1.9833*10.32053501/sqrt(104)

Confidence interval = 75.67307692 ± 2.0071

Lower limit = 75.67307692 - 2.0071 = 73.67

Upper limit = 75.67307692 + 2.0071 = 77.68

Confidence interval = (73.67, 77.68)