In: Statistics and Probability
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
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.