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 equals=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?

7​, 8​, 2​, 8​, 4​, 4, 6​, 7​, 7​, 10​, 6​, 8

__< μ <__

  

Answer 1

SOLUTION:

From given data,

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 equals=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?

7​, 8​, 2​, 8​, 4​, 4, 6​, 7​, 7​, 10​, 6​, 8

Mean = = x / n = (7+8+2+8+4+4+6+7+7+10+ 6+8) / 12 = 77 / 12 = 6.417

Standard deviation = s = sqrt ((7-6.417)^2+(8-6.417)^2+(2-6.417)^2+(8-6.417)^2+(4-6.417)^2+(4-6.417)^2+(6-6.417)^2+(7-6.417)^2+(7-6.417)^2+(10-6.417)^2+ (6-6.417)^2+(8-6.417)^2) /(12-1)

= 0.6613

Compute the degree of freedom

df = n-1

= 12-1

= 11

95% confidence level

95% = 95/100 = 0.95

= 1-0.95 = 0.05

/ 2 = 0.05 /2 = 0.025

From the t-distribution table (As shown below) , the critical value at 0.05 level of the significance for 11 degrees of freedom about two tailed is 2.2010.

Determine the margin of error using the following formula.

E = * (s / sqrt (n))

E = 2.2010* (0.6613 / sqrt (12))

E = 0.42017

Determine the 95% confidence interval using the following formula,

- E <    <  + E

6.417 - 0.42017 <   < 6.417 + 0.42017

5.99683 <   < 6.83717

5.9968 <   < 6.8372

Therefore , the 95% confidence interval for mean amount of attractiveness of the population of all adult females lies between  5.9968 <   < 6.8372