Question
Asked Nov 5, 2019
35 views

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

90​%

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

Ratings
7
7
3
9
4
6
8
8
8
8
6
9

What is the confidence interval for the population mean
mu μ​?
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Expert Answer

Step 1

Find the distribution that has to be used to construct the confidence interval in the given situation:

The data represents the attractiveness rating of male subjects to their female dates.

The sample size is n = 12.

Assume that the population of attractiveness rating of male subjects to their female dates is normally distributed.

The required conditions for using t distribution to estimate the confidence interval about mean is given below:

  • The population standard deviation σ must be unknown.
  • Either the sample size (n) must be greater than 30 or the population must be normally distributed.

Here, the population standard deviation is unknown.

Step 2

The population from which the sample is drawn is assumed to be normally distributed.

Thus, the t–distribution is used to construct the confidence interval for the population mean in the given situation.

The approximate 100*(1–α)% confidence interval for the population mean will be obtained using the formula given below:

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Image Transcriptionclose

CI t <u<τ+ t, X Here, is sample mean, n is sample size s is sample standard deviation and is two tailed criti cal value of t-distribution at n-1 degrees of freedom

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Step 3

Find the sample mean and standard deviation of attractiveness rating:

Excel procedure to find the mean and standard deviation of attractiveness rating:

Step 1: Enter the values of attractiveness rating from A2:A13.

Step 2: Obtain the sample mean in c...

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Image Transcriptionclose

Sample mean Sample standard deviation 1.88092498 6.91666667

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Tagged in

Math

Statistics

Hypothesis Testing

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