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Chapter 8: Q4 (page 408)
P-Value Find the P-value in a test of the claim that the mean annual income of a CIA agent is greater than $81,623 (based on data from payscale.com) given that the test statistic is t = 1.304 for a sample of 40 CIA agents.
The p-value is equal to 0.10.
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PowerFor a hypothesis test with a specified significance level , the probability of a type I error is, whereas the probability of a type II error depends on the particular value ofpthat is used as an alternative to the null hypothesis.
a.Using an alternative hypothesis ofp< 0.4, using a sample size ofn= 50, and assumingthat the true value ofpis 0.25, find the power of the test. See Exercise 34 “Calculating Power”in Section 8-1. [Hint:Use the valuesp= 0.25 andpq/n= (0.25)(0.75)/50.]
b.Find the value of , the probability of making a type II error.
c.Given the conditions cited in part (a), find the power of the test. What does the power tell us about the effectiveness of the test?
Estimates and Hypothesis Tests Data Set 3 “Body Temperatures” in Appendix B includes sample body temperatures. We could use methods of Chapter 7 for making an estimate, or we could use those values to test the common belief that the mean body temperature is 98.6°F. What is the difference between estimating and hypothesis testing?
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?
A formal hypothesis test is to be conducted using the claim that the mean height of men is equal to 174.1 cm.
a. What is the null hypothesis, and how is it denoted?
b. What is the alternative hypothesis, and how is it denoted?
c. What are the possible conclusions that can be made about the null hypothesis?
d. Is it possible to conclude that “there is sufficient evidence to support the claim that the mean height of men is equal to 174.1 cm”?
t Test Exercise 2 refers to a t test. What is the t test? Why is the letter t used? What is unrealistic about the z test methods in Part 2 of this section?
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