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 ​(1=not​attractive;10=extremely ​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?

6​,8​,3​,8​,6​,4,7​,8​,9,10,5,9

Q) What is the confidence interval for the population mean μ​? _____ < μ​ < ______ ( round to one decimal place as needed )

Answer 1

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 6.916666667

S = 2.1514618

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 = 6.916666667 ± 1.7959*2.1514618/sqrt(12)

Confidence interval = 6.916666667 ± 1.1154

Lower limit = 6.916666667 - 1.1154 = 5.8

Upper limit = 6.916666667 + 1.1154 = 8.0

Confidence interval = (5.8, 8.0)

5.8 < µ < 8.0