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Chapter 8: Q. 10 (page 392)

Determine the critical value(s) for a one-mean z-test at the 1%significance level if the test is

a. right tailed. b. left tailed

c. two tailed

Short Answer

Expert verified

For right tailed, z0.01=2.33

For left tailed, z0.01=-2.33

For two tailed,±z0.01=±2.575

Step by step solution

01

Step 1. Right tailed

We determine the critical value for a one-mean z-test at the 1%significance level if the test is right tailed.

When α=0.01, we find normal distribution tables, the critical value of z0.01=2.33as shown in the figure below.

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Most popular questions from this chapter

Using Confidence Intervals to Test Hypotheseswhen analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

a.Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

b.Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

c.Use the sample data to construct a 95% confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals 0.1?

d.Compare the results from the critical value method, the P-value method, and the confidence interval method. Do they all lead to the same conclusion?

Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected 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.

Is the Diet Practical? When 40 people used the Weight Watchers diet for one year, their mean weight loss was 3.0 lb and the standard deviation was 4.9 lb (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Reduction,” by Dansinger et al., Journal of the American Medical Association, Vol. 293, No. 1). Use a 0.01 significance level to test the claim that the mean weight loss is greater than 0. Based on these results, does the diet appear to have statistical significance? Does the diet appear to have practical significance?

Testing Claims About Proportions. In Exercises 9–32, 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.

Births A random sample of 860 births in New York State included 426 boys. Use a 0.05 significance level to test the claim that 51.2% of newborn babies are boys. Do the results support the belief that 51.2% of newborn babies are boys?

Interpreting Power For the sample data in Example 1 “Adult Sleep” from this section, Minitab and StatCrunch show that the hypothesis test has power of 0.4943 of supporting the claim that μ<7 hours of sleep when the actual population mean is 6.0 hours of sleep. Interpret this value of the power, then identify the value of βand interpret that value. (For the t test in this section, a “noncentrality parameter” makes calculations of power much more complicated than the process described in Section 8-1, so software is recommended for power calculations.)

Confidence interval Assume that we will use the sample data from Exercise 1 “Video Games” with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing the claim, what confidence level should be used for the confidence interval? If the confidence interval is found to be 21.1 sec < μ< 191.4 sec, what should we conclude about the claim?
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