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.
================================
Cheers,
Stan H.
|
|
|
