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Alinara [238K]
3 years ago
5

A sample of 51 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square val

ues to be used for this interval estimation are
a. -1.96 and 1.96
b. 32.357 and 71.420
c, 34.764 and 67.505
d. 12.8786 and 46.9630

Business
1 answer:
lorasvet [3.4K]3 years ago
5 0

Answer:

Correct option: (b) 32.357 and 71.420

Explanation:

The confidence interval for population variance <em>σ</em>² is:

\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1) }}\leq  \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{(1-\alpha/2), (n-1) }}

Given:

n=51\\\alpha =1-0.95=0.05

Compute the critical values of chi-square as follows:

\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.025,50}=71.42

\chi^{2}_{(1-\alpha/2), (n-1)}=\chi^{2}_{0.975,50}=32.36

Use the chi-square table for the critical value.

Thus, the critical values are 32.36 and 71.42.

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