SOLUTION: A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 106.8​, and the sample standard deviation is found to be 22.7. Is the populatio

Algebra ->  Probability-and-statistics -> SOLUTION: A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 106.8​, and the sample standard deviation is found to be 22.7. Is the populatio      Log On


   

Question 1057824: A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 106.8​, and the sample standard deviation is found to be 22.7. Is the population mean greater than 100 at the alpha=0.05 level of​ significance?
Answer by solve_for_x(190) About Me  (Show Source):
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The hypotheses are:

Null: H0: µ = 100

Alternative: H1: µ > 100

This is a one-tailed, right-sided test with alpha = 0.05

The test statistic is:

z = (x-bar - µ) / (s/√n) = (106.8 - 100) / (22.7/√40) = 1.8946

Consulting a table of the normal distribution, or a statistical calculator, the p-value
that corresponds to z = 1.8946 is p = 0.02907.

Since this p-value is less than the level of significance (0.05), the decision is to reject
the null hypothesis.

There is sufficient evidence at the 0.05 level of significance to support a claim that the
population mean is greater than 100.