SOLUTION: . A random sample of 41 observations was selected from a normally distributed population. The sample mean was x = 61, and the sample variance was s^2 = 18.0. Does the sample show s

Question 250039: . A random sample of 41 observations was selected from a normally distributed population. The sample mean was x = 61, and the sample variance was s^2 = 18.0. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 4 at the 0.05 level of significance? Use the p-value method.
� State the null and alternate hypotheses
� Determine which test statistic applies, and calculate it
� Determine the corresponding probability, and compare to a
� State your decision: Should the null hypothesis be rejected?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A random sample of 41 observations was selected from a normally distributed population.
The sample mean was x = 61, and the sample variance was s^2 = 18.0.
Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 4 at the 0.05 level of significance?
Use the p-value method.
� State the null and alternate hypotheses
Ho: sigma = 4
H1: sigma is not equal to 4
----------------------------------
� Determine which test statistic applies, and calculate it
Chi-Sq = (n-1)s^2/sigma^2 = 40*18/16 = 45
� Determine the corresponding probability, and compare to a ?????
left-tail critical value:24.433
right-tail critical value: 59.342
� State your decision: Should the null hypothesis be rejected?
The test stat is in the fail to reject interval.
Ho should not be rejected.
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Cheers,
Stan H.

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