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)   (Show Source):
You can put this solution on YOUR website! 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.
|
|
|
