Question 269290: A random sample of 51 observations was selected from a normally distributed population. The sample mean was xbar = 64, and the sample variance was s2 = 48.0. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 9 at the 0.02 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
· 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 51 observations was selected from a normally distributed population.
The sample mean was xbar = 64, and the sample variance was s2 = 48.0.
Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 9 at the 0.02 level of significance?
Use the p-value method.
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· State the null and alternate hypotheses
Ho: sigma^2 = 81
H1: sigma^2 is not equal to 81
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· Determine which test statistic applies, and calculate it
Chi-Sq = (51-1)48/81 = 29.04
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· Determine the corresponding probability, and compare to ?
p-value = 2P(Chi-sq > 29.04 with df = 50) is approximately 2(0.005)= 0.01
Note: I don't have technology that will so me the exact p-value.
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· State your decision: Should the null hypothesis be rejected?
Since my p-value is less than 2%, I would reject Ho.
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sigma^2 is not 81, so sigma is not 9
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Cheers,
Stan H.
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