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melamori03 [73]
3 years ago
9

A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the

test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the standard deviation, σ, of the scores of all subjects.a. 17.5 < σ < 27.8b. 17.2 < σ < 27.2c. 285.61 < σ <858.49d. 16.6 < σ < 28.6e. 16.9 < σ < 29.3
Mathematics
1 answer:
Crazy boy [7]3 years ago
6 0

Answer: e. 16.9<\sigma<29.3

Step-by-step explanation:

As per given , we have

n= 27 , \overline{x}=76.2  , s=21.4

Critical value using Chi-square table:-

\chi^2_{\alpha/2, n-1}=\chi^2_{0.025, 26}=41.92317010\\\\ \chi^2_{1-\alpha/2, n-1}=\chi^2_{0.975, 26}=13.84390498

Confidence interval for standard deviation:

\sqrt{\dfrac{(n-1) s^2}{\chi^2_{\alpha/2, n-1}}}< \sigma

Hence, the 95% confidence interval for the standard deviation, σ, of the scores of all subjects : 16.9

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