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 ​95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult​ females? 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9 What is the confidence interval for the population mean ​μ? <μ

Answer 1

Confidence Interval = ( 5.6 < μ < 8.2 )

The interval shows that the mean attractiveness is Above average on a scale of 1 to 10

Explanation:

Data Given : 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9

a) construct a confidence interval at a 95% confidence level

confidence interval = x ± tcritical ( s / √ n ) ------ ( 1 )

n = 12

μ (mean) = ( 5+8+2+8+7+6+6+8+9+9+6+9 ) / 12 ≈ 6.92

std ( s ) = √ 1/11 *∑( xi- X )^2

= √ 1/11 * ( 5 - 6.92)^2 + ( 8 - 6.92)^2 + ( 2 - 6.92)^2 + ( 8 - 6.92)^2 + ( 7-6.92)^2 + ( 6 - 6.92)^2 + (6 - 6.92 )^2 + ( 8 - 6.92 )^2 + ( 9 - 6.92)^2 + ( 9 - 6.92)^2 + ( 6 - 6.92 )^2 + ( 9 - 6.92 )^2

= √ 1/11 * 46.92 = 2.07

tcritical at ∝ 0.05 , df = 11 = 2.20

Back to equation 1

6.92 ± 2.2 ( 2.07 / √ 12 )

( 6.92 ± 1.31 )

Confidence Interval = ( 5.6 < μ < 8.2 )