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 99​% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult​ females?

7,7,3,9,6,5,7,9,8,9,4,9

What is the confidence interval for the population mean μ​?

____< μ <____

​(Round to one decimal place as​ needed.)

Answer 1

Solution :

Given that,

sample size = n = 12

Point estimate = sample mean = = Xi / n

= (7+7+3+9+6+5+7+9+8+9+4+9)/12

= 83/12

= 6.9

sample standard deviation = s = ( Xi - )² / n - 1

= ((7-6.9)²+(7-6.9)²+(3-6.9)²​​​​​​​+(9-6.9)²​​​​​​​+(6-6.9)²​​​​​​​+(5-6.9)²​​​​​​​+(9-6.9)²​​​​​​​+(8-6.9)²​​​​​​​+(9-6.9)²​​​​​​​+(4-6.9)²​​​​​​​+(9-6.9)²​​​​​​​ / 12 - 1

=22.715 / 11

= 2.07

Degrees of freedom = df = n - 1 = 11

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,11 = 3.106

Margin of error = E = t_/2,df * (s /n)

= 3.106 * (2.07 / 12)

= 1.9

The 99% confidence interval estimate of the population mean is,

- E < < + E

6.9 - 1.9 < < 6.9 +1.9

5.0 < < 8.8