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Chapter 8: Q21 (page 372)

Critical Values. In Exercises 21鈥�24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of = 0.05, should we reject H0or should we fail to reject H0?

Exercise 17

Short Answer

Expert verified

a. The critical value is equal to 1.645.

b. The decision of the statistical test is to fail to rejectH0

Step by step solution

01

Given information

A test statistic value of z=1.00 is obtained, and the claim to be tested is p>0.3.

02

Hypotheses and tail of the test

In correspondence with the given claim, the following hypotheses are set up:

Null Hypothesis: p=0.3

Alternative Hypothesis: p>0.3

Since there is a greater than sign in the alternative hypothesis, the test is right-tailed.

03

Critical value

a.

Referring to the standard normal table, the critical value of z corresponding to the right-tailed test at 伪=0.05 is equal to 1.645.

04

Decision about the test

b.

If the test statistic value is greater than the critical value, then the null hypothesis is rejected.

Here, the test statistic value (1.00) is less than the critical value (1.645), so the decision is to fail to reject the null hypothesis.

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Most popular questions from this chapter

This exercise contain graphs portraying the decision criterion for a one-mean 2-test. The curve in each graph is the normal curve for the test statistic under the assumption that the null hypothesis is true. For each exercise, determine the

a. rejection region.

c. critical value(s).

b. nonrejection region.

d. significance level.

e. Construct a graph similar to that in Fig. 9.3 on page 361 that depicts your results from parts (a)-(d).

f. Identify the hypothesis test as two tailed, left tailed or right tailed.

Testing Claims About Proportions. In Exercises 9鈥�32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

M&Ms Data Set 27 鈥淢&M Weights鈥� in Appendix B lists data from 100 M&Ms, and 27% of them are blue. The Mars candy company claims that the percentage of blue M&Ms is equal to 24%. Use a 0.05 significance level to test that claim. Should the Mars company take corrective action?

Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Course Evaluations Data Set 17 鈥淐ourse Evaluations鈥� in Appendix B includes data from student evaluations of courses. The summary statistics are n = 93, x = 3.91, s = 0.53. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 4.00.

Vitamin C and Aspirin A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin. When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin?

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then the conclusion about the null hypothesis, as well as the final conclusion that address the original claim. Assume that a simple random sample is selected from a normally distributed population.

Pulse Rates of Women Repeat the preceding exercise using the pulse rates of women listed in Data Set 1 鈥淏ody Data鈥� in Appendix B. For the sample of pulse rates of women, n= 147 and s= 12.5. See the accompanying JMP display that results from using the original list of pulse rates instead of the summary statistics. (Hint:The bottom three rows of the display provide P-values for a two-tailed test, a left-tailed test, and a right-tailed test, respectively.) What do the results indicate about the effectiveness of using the range rule of thumb with the 鈥渘ormal range鈥� from 60 to 100 beats per minute for estimating s in this case?
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