SOLUTION: A random sample of 49 observations was selected from a normally distributed population. The sample mean was x bar = 98.5, and the sample variance was s2 = 37.4. Does this sample sh

Question 975352: A random sample of 49 observations was selected from a normally distributed population. The sample mean was x bar = 98.5, and the sample variance was s2 = 37.4. Does this sample show sufficient reason to conclude that the population standard deviation is not equal to 7 at the 0.05 significance level?
(ii) Find χ2solid black star icon. (Give your answer correct to two decimal places.)
36.64
(iii) Find the p-value. (Give your answer bounds exactly.)
< p <
(b) State the appropriate conclusion.
(a) Reject the null hypothesis, there is not significant evidence that the population standard deviation differs from 7.
(b) Reject the null hypothesis, there is significant evidence that the population standard deviation differs from 7.
(c) Fail to reject the null hypothesis, there is not significant evidence that the population standard deviation differs from 7.
(d) Fail to reject the null hypothesis, there is significant evidence that the population standard deviation differs from 7.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
standard deviation is 6.1155
This is a two-tailed test determining whether the sample sd= population sd
or the ratio of 37.4/49= 0.763 (using the variances) differs significantly from 1. The test statistic follows a Chi-Square distribution with 48 degrees of freedom. Because the value can be in either direction from 1, both ends of the distribution are considered.
Test statistic=(n−1)(s/(sigma)2
This is (48)(6.1155-7)^2=37.548
Chi square distribution is followed with 48 degrees of freedom.
The critical values are about 30 on the low end and about 69 on the upper end. We fail to reject the null hypothesis and conclude there is insufficient evidence to reject Ho that says the sample sd=population sd.
0.10 C is the answer. If you were ever guessing, A and D as written are always wrong.

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