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? 7.9.1.9.4,6,6,9, 7, 8, 6,9 D What is the confidence interval for the population mean u? <<(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. O 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. OB. We are 99% confident that the interval from to actually contains the true mean attractiveness rating of all adult females. (Round to one decimal place as needed.) OC. We are confident that 99% of all adult females have attractiveness ratings between and

Answer 1

The given data is summarized as

Sample size(n)=12

Sample mean()=6.75

T

Sample SD(s)=2.416797

The 99% confidence interval is given by

$(\bar{x}\pm\frac{s}{\sqrt{n}}\;t_{0.005,n-1})$

$i.e.\;\;(6.75\pm\frac{2.416797}{\sqrt{12}}\;t_{0.005,11})$

$i.e.\;\;(6.75\pm\frac{2.416797}{\sqrt{12}}*3.105807)$

$i.e.\;\;(6.75\pm2.166825883)$

$i.e.\;\;4.6\leq \mu \leq 8.9$

By definition of confidence interval, the correct option is option B.

i.e. We are 99% confident that the interval from 4.6 to 8.9 actually containes the true mean attractiveness rating of all adult of all adult females.

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