Basic Computation: Testing m1  m2 Two populations have normal distributions.

The fi rst has population standard deviation 2 and the second has population standard deviation 3.

A random sample of 16 measurements from the fi rst population had a sample mean of 20.

An independent random sample of 9 measurements from the second population had a sample mean of 19.

Test the claim that the population mean of the fi rst population exceeds that of the second. Use a 5% level of signifi cance.

(a) Check Requirements What distribution does the sample test statistic follow?

Explain.

(b) State the hypotheses.

(c) Compute x1  x2 and the corresponding sample test statistic.

(d) Find the P-value of the sample test statistic.

(e) Conclude the test.

(f) Interpret the results.

(g) Find a 90% confi dence interval for m1  m2. Explain the meaning of the confi dence interval in the context of the problem.

Please provide the following information for Problems 11–22, part (a):

(i) What is the level of signifi cance? State the null and alternate hypotheses.

(ii) Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?

(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(iv) Based on your answers in parts (i) – (iii), will you reject or fail to reject the null hypothesis? Are the data statistically signifi cant at level a?

(v) Interpret your conclusion in the context of the application.

Note: For degrees of freedom d.f. not in the Student’s t table, use the closest d.f.

that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount, and therefore produce a slightly more “conservative” answer.

Answers may vary due to rounding.