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 ​(1equalsnot ​attractive; 10equalsextremely ​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? 5​, 7​, 1​, 9​, 4​, 6​, 6​, 9​, 8​, 9​, 4​, 8 What is the confidence interval for the population mean mu​? nothingless thanmuless than nothing ​(Round to one decimal place as​ needed.) What does the confidence interval tell about the population of all adult​ females? Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice. A. The results tell nothing about the population of all adult​ females, because participants in speed dating are not a representative sample of the population of all adult females. B. We are confident that 99​% of all adult females have attractiveness ratings between nothing and nothing. ​(Round to one decimal place as​ needed.) C. We are 99​% confident that the interval from nothing to nothing actually contains the true mean attractiveness rating of all adult females. ​(Round to one decimal place as​ needed.)

Answer 1

Solution:

Given:

c = confidence level = 99%

Sample: 5​, 7​, 1​, 9​, 4​, 6​, 6​, 9​, 8​, 9​, 4​, 8

Part a) We have to construct a confidence interval using a 99​% confidence level for mean attractiveness ratings of the population of all adult​ females.

Formula:

where

Thus we need to make following table:

x	x^2
5	25
7	49
1	1
9	81
4	16
6	36
6	36
9	81
8	64
9	81
4	16
8	64

and find t_c value for c = 99% confidence level

df = n - 1 = 12 - 1 = 11

Two tail area = 1 -c = 1 - 0.99 = 0.01

t critical value = t_c = 3.106

Thus

Thus

Round to one decimal place as​ needed.

Part b) What does the confidence interval tell about the population of all adult​ females?

C. We are 99​% confident that the interval from 4.1 to 8.6 actually contains the true mean attractiveness rating of all adult females.