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Chapter 8: Q24 (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 20

Short Answer

Expert verified

a. The critical values are -1.96 and 1.96.

b. The decision of the statistical test is to fail to reject the null hypothesis.

Step by step solution

01

Given information

A test statistic value of z=-1.94 is obtained, and the claim to be tested is p=38.

02

Hypotheses and tail of the test

The hypotheses are as follows:

Null Hypothesis: p=38

Alternative Hypothesis: p鈮�38

Since there is a not equal to sign in the alternative hypothesis, the test is two-tailed.

03

Critical value

a.

Referring to the standard normal table, the critical values of z corresponding to the two-tailed test at 伪=0.05are -1.96 and 1.96.

04

Decision about the test

b.

If the absolute value of the test statistic is greater than the critical value, then the null hypothesis is rejected; otherwise, not.

Since the absolute value of the test statistic is less than the critical value, the decision is to fail to reject the null hypothesis.

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Most popular questions from this chapter

Fill in the following blanks.
a. Thet-test is..................... to moderate violations of the normality assumption.
b. The t-test can sometimes be unduly affected by outliers because the sample mean and sample standard deviation are not................................. to outliers.

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Is Nessie Real? This question was posted on the America Online website: Do you believe the Loch Ness monster exists? Among 21,346 responses, 64% were 鈥測es.鈥� Use a 0.01 significance level to test the claim that most people believe that the Loch Ness monster exists. How is the conclusion affected by the fact that Internet users who saw the question could decide whether to respond?

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 18

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.

Finding Critical t Values When finding critical values, we often need significance levels other than those available in Table A-3. Some computer programs approximate critical t values by calculating t=df脳eA2/df-1where df = n-1, e = 2.718, A=z8脳df+3/8脳df+1, and z is the critical z score. Use this approximation to find the critical t score for Exercise 12 鈥淭ornadoes,鈥� using a significance level of 0.05. Compare the results to the critical t score of 1.648 found from technology. Does this approximation appear to work reasonably well?
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