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Chapter 8: Q. 9.55 (page 370)
We have given the P-value for a hypothesis test. For each exercise determine the strength of the evidence against null hypothesis.
Given
The P-value is 0.06, which is in the range of 0.05 to 0.10.
Thus null hypothesis is strongly rejected.
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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.
Super Bowl Wins Through the sample of the first 49 Super Bowls, 28 of them were won by teams in the National Football Conference (NFC). Use a 0.05 significance level to test the claim that the probability of an NFC team Super Bowl win is greater than one-half.
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.
Cans of Coke Data Set 26 “Cola Weights and Volumes” in Appendix B includes volumes (ounces) of a sample of cans of regular Coke. The summary statistics are n = 36, x = 12.19 oz, s = 0.11 oz. Use a 0.05 significance level to test the claim that cans of Coke have a mean volume of 12.00 ounces. Does it appear that consumers are being cheated?
Critical Values. In Exercises 21–24, 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 or should we fail to reject ?
Exercise 19
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?
Identifying and . In Exercises 5–8, do the following:
a. Express the original claim in symbolic form.
b. Identify the null and alternative hypotheses.
Pulse Rates Claim: The standard deviation of pulse rates of adult males is more than 11 bpm. For the random sample of 153 adult males in Data Set 1 “Body Data” in Appendix B, the pulse rates have a standard deviation of 11.3 bpm.
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