Question

For a certain variable x, we want to test if the true mean of x is less than 32, at significance level 0.05. A sample of size 121 gave a sample mean of 28, and a sample standard deviation of 15.4. Is there sufficient evidence here to conclude that the true mean is indeed less than 32? Use the p-value approach.

True/False: The test statistic is -2.84.
a) True
b) False

Answer 1

The test statistic is -2.84.

Step-by-step explanation:

The test statistic is -2.84, which means that the sample mean is 2.84 standard deviations below the population mean. To determine if there is sufficient evidence to conclude that the true mean is less than 32, we need to compare this test statistic to the critical value for a one-tailed test with a significance level of 0.05. If the test statistic falls in the rejection region (below the critical value), then we can conclude that there is sufficient evidence to support the claim that the true mean is less than 32. Therefore, the statement a) True is correct.