For each of the following samples that were given an experimental treatment, test whether these samples represent populations that are different from the general population: A. a sample of 10 with a mean of 44. B.a sample of 1 with a mean of 48. The general population of individuals has a mean of 40, a standard deviation of 6, and follows a normal curve. For each sample, carry out a Z test using the five steps hypothesis testing with a two-tailed test at the .05 significance level, and make a drawing of the distributions involved.

Question

For each of the following samples that were given an experimental treatment, test whether these samples represent populations that are different from the general population: A. a sample of 10 with a mean of 44. B.a sample of 1 with a mean of 48. The general population of individuals has a mean of 40, a standard deviation of 6, and follows a normal curve.  For each sample, carry out a Z test using the five steps hypothesis testing with a two-tailed test at the .05 significance level, and make a drawing of the distributions involved.

MathGuru · Answer

Here are a few hints:

1. Use a one-sample z-test for both A and B, which is:
z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

2. Find the critical or cutoff value to reject the null using a z-table for .05 level of significance for a two-tailed test. If the test statistic exceeds the critical value you find in the table, reject the null and conclude a difference. If the test statistic does not exceed the critical value you find in the table, do not reject the null. You cannot conclude a difference in this case.

I hope this will help get you started.