Question

In a study of speed​ dating, male subjects were asked to rate the attractiveness of their female​ dates, and a sample of the results is listed below ​(1equalsnot ​attractive; 10equalsextremely ​attractive). Construct a confidence interval using a 90​% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult​ females? 5​, 7​, 2​, 9​, 7​, 6​, 6​, 8​, 9​, 10​, 3​, 8

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 = 6.666666667

S = 2.424621183

n = 12

df = n – 1 = 11

Confidence level = 90%

Critical t value = 1.7959

(by using t-table)

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

Confidence interval = 6.666666667 ± 1.7959*2.424621183/sqrt(12)

Confidence interval = 6.666666667 ± 1.2570

Lower limit = 6.666666667 - 1.2570 = 5.41

Upper limit = 6.666666667 + 1.2570 = 7.92

Confidence interval = (5.41, 7.92)

We are 90% confident that the mean attractiveness ratings will lies between 5.41 and 7.92.