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In Exercises 9鈥16, assume that each sample is a simplerandom sample obtained from a population with a normal distribution.

Speed Dating In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Construct a 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained.

5 8 3 8 6 10 3 7 9 8 5 5 6 8 8 7 3 5 5 6 8 7 8 8 8 7

Short Answer

Expert verified

The 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained is1.5<<2.6.

Step by step solution

01

Given information

The sample number of female subjects that were asked to rate the attractiveness of their male dates is n=26.

The level of confidence is 95%.

02

Compute the critical values

The degrees of freedom are computed as follows:

df=n-1=26-1=25

The level of confidence is 95%,which implies the level of significance is 0.05.

Using the Chi-square table, the critical values at 0.05 level of significance and 25 degrees of freedom are L2=13.12and R2=40.646.

03

Compute the mean and standard deviation

The confidence interval for the standard deviation is given as follows:

(n-1)s2R2<<(n-1)s2L2

Let x represents the sample observations.

The mean value is computed as follows:

x=xn=5+8+3+8+...+8+726=6.577

The standard deviation is computed as follows:

s=x-x2n-1=5-6.5772+8-6.5772+3-6.5772+...+7-6.577226-1=1.880

04

Construct the confidence interval

The 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained is computed as follows:

n-1s2R2<<n-1s2L226-11.880240.646<<26-11.880213.121.4744<<2.5951.5<<2.6

Therefore, the 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained is role="math" localid="1648111628961" 1.5<<2.6
.

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