Environmentalists measure the pH levels of30 samples of acid rain in a certain region. The data are as follows:

4.8	4.4	5.0	4.9	5.6	4.3	5.2	4.9	5.4	4.4	4.0	4.6	5.3	4.4	5.7
4.8	4.3	4.6	4.1	5.0	4.9	4.2	4.5	5.3	4.9	4.6	4.7	5.1	4.9	5.2

The population standard deviation of acid rain pH levels is known to be 0.54. (a) We have no knowledge about whether pH levels follow a normal distribution. Why is it nevertheless appropriate to use inference methods which rely on the assumption of normality? (b) Construct a 93% confidence interval for the true mean pH level of acid rain in the region. Explain how you find the critical valuez*. (c) Provide an interpretation of the interval in (b). (d)Conduct a hypothesis test at the 7% level of significance to determine whether the true mean pH level of acid rain in a certain region differs from 5.0. Use the critical value method. Show all of your steps, including the hypotheses, the decision rule, the calculation of the test statistic, and a properly worded conclusion. (e) Suppose you had used theP-value methodto conduct the test in (d). What is the P-value of the test? What would be your conclusion, and why? (f) Interpret the meaning of the P-value you calculated in (e). (g) Verify your results for the test usingJMP. Type the data values in a column titledpH level. Go toAnalyze > Distribution. Under thered arrow, selectTest Mean. Enter 5 for the hypothesized mean and 0.54 as the true standard deviation.You do not need toattach the output to your assignment. What is the exact P-value of the test, as given byJMP? (h) Could the interval in (b) have been used to conduct the test in (d)? If no, explain why not. If yes, explain why, and explain what your conclusion would have been and why.

An experimenter is concerned about radiation levels in her research laboratory. Radiation levels are known to follow a normal distribution. A random sample of 12 radiation measurements is taken at different locations in the laboratory, the values of which are shown below:

427

410

397

433

389

426

412

408

394

415

399

446

The mean and standard deviation for these twelve measurements are 413and 17.273, respectively.

(a)Calculate a 90% confidence intervalfor the true mean radiation level in the laboratory.(Roundvalues totwodecimal places.)

(b)A roomis only considered safe to work in if themean radiation level is 400 or lower. The experimenter would like to conduct a hypothesis test at the 10% level of significanceto determine if the laboratory is unsafe. Whatare the appropriate hypotheses for the appropriate test of significance?

(c) What is the value of the appropriate test statistic?

(d) What is the P-value of the test?

(e) UseJMPto verify your calculations. To conduct attestinJMP, enter the data values into a column titledRadiation Level.Select Analyze > Distribution, clickRadiation Level, thenY, Columns, thenOK. Under thered arrow, selectTest Mean. Enter 400 as the hypothesized mean, and leave the standard deviation box empty. (This tellsJMPwe don't know the population standard deviation, so it will know to doattestrather than aztest.) You do not need toattach the output to your assignment.What is the exact P-value of the test (tofourdecimal places)?

(f) What is the conclusion of thetest?

(g) Suppose you had instead used the critical value method to conduct the test. Whatwould bethe decision rule and conclusion?