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Chapter 8: Q2 (page 396)
df If we are using the sample data from Exercise 1 for a t-test of the claim that the population mean is greater than 90sec, What does df denote, and what is its value?
The degrees of freedom of the data denote the number of independent observations in it. The value is 11.
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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?
P-Values. In Exercises 17–20, do the following:
a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.
b. Find the P-value. (See Figure 8-3 on page 364.)
c. Using a significance level of = 0.05, should we reject or should we fail to reject ?
The test statistic of z = 1.00 is obtained when testing the claim that .
Final Conclusions. In Exercises 25–28, use a significance level of = 0.05 and use the given information for the following:
a. State a conclusion about the null hypothesis. (Reject or fail to reject .)
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
Original claim: Fewer than 90% of adults have a cell phone. The hypothesis test results in a P-value of 0.0003.
Lead in Medicine Listed below are the lead concentrations (in ) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States (based on data from “Lead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet,” by Saper et al., Journal of the American Medical Association,Vol. 300, No. 8). Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 .
3.0 6.5 6.0 5.5 20.5 7.5 12.0 20.5 11.5 17.5
Finding P-values. In Exercises 5–8, either use technology to find the P-value or use Table A-3 to find a range of values for the P-value.
8. Tornadoes. The claim is that for the widths (yd) of tornadoes, the mean is yd. The sample size is n = 21 and the test statistic is t = -0.024.
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