SOLUTION: A random sample has 42 values. The sample mean is 9.5 and the sample standard deviation is 1.5. Use a level of significance of 0.02 to conduct a left-tailed test of the claim that

Question 1120542: A random sample has 42 values. The sample mean is 9.5 and the sample standard deviation is 1.5. Use a level of significance of 0.02 to conduct a left-tailed test of the claim that the population mean is 10.0.
A) Are the requirements met to run a test like this?
B) What are the hypotheses for this test?
C) Compute the test statistic and the p-value for this test.
D) What is your conclusion at the 0.02 level of significance.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Assume random sample, sd measured in sample can be considered an unbiased estimator of the population sd, normal distribution of population, or at least close enough to be considered as such.
Ho: mean is 10
Ha: mean isn't 10
alpha 0.02
test stat is t 0.99,df=41 : (x bar-mean)*s/ sqrt (n)
Critical value is |t|>2.42
Therefore -0.5/1.5/sqrt(42)= -2.16
Fail to reject, p-value 0.037 > 0.02
Insufficient evidence to state that the mean is not 10.

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