In Exercises 5–20, assume that the two samples are independent simple random samples selected from
15. Are Quarters Now Lighter? Weights of quarters are carefully considered in the design of the vending machines that we have all come to know and love. Data Set 29 “Coin Weights” in Appendix B includes weights of a sample of pre-1964 quarters (n = 40,
a. Use a 0.05 significance level to test the claim that pre-1964 quarters have a mean weight that is greater than the mean weight of post-1964 quarters.
b. Construct a confidence interval appropriate for the hypothesis test in part (a).
c. Do post-1964 quarters appear to weigh less than before 1964? If so, why aren’t vending machines affected very much by the difference?
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Chapter 9 Solutions
Elementary Statistics (13th Edition)
- In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1 − 1 and n2 − 1.) IQ and Lead Exposure Data Set 7 “IQ and Lead” in Appendix B lists full IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The statistics are summarized below. a. Use a 0.05 significance level to test the claim that the mean IQ score of people with low blood lead levels is higher than the mean IQ score of people with high blood lead levels. b. Construct a confidence interval appropriate for the hypothesis test in part (a). c. Does exposure to lead appear to have an effect on IQ scores?arrow_forwardChapter 6, Section 5, Exercise 236 Use a t-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d=x1-x2.Test H0 : μd=0 vs Ha : μd≠0 using the paired difference sample results x¯d=10.51, sd=11.6, nd=25. Give the test statistic and the p-value.Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.test statistic = Enter your answer; test statisticp-value = Enter your answer; p-value Give the conclusion using a 5% significance level. Reject H0. Do not reject H0.arrow_forwardChapter 6, Section 4-HT, Exercise 212 Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal.Test H0 : μT=μC vs Ha : μT<μC using the fact that the treatment group (T) has a sample mean of 8.6 with a standard deviation of 4.1 while the control group (C) has a sample mean of 11.2with a standard deviation of 3.4. Both groups have 25 cases. (a) Give the test statistic and the p-value.Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.test statistic = p-value = (b) What is the conclusion of the test at a 5% significance level? Reject H0. Do not reject H0.arrow_forward
- A U.S. Food Survey showed that Americans routinely eat beef in their diet. Suppose that in a study of 49 consumers in Illinois and 64 consumers in Texas the following results were obtained from two samples regarding average yearly beef consumption: Illinois Texas = 49 = 64 = 54.1lb = 60.4lb S1 = 7.0 S2 = 8.0 Formulate a hypothesis so that, if the null hypothesis is rejected, we can conclude that the average amount of beef eaten annually by consumers in Illinois is significantly less than that eaten by consumers in Texas.arrow_forwardIn a hypothesis test with hypotheses Ho: μ ≤ 54 and H1: μ > 54, a random sample of 24 elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4. The test is to be made at the 10% significance level. Assume the population is normally distributed. What is the critical value of t ?arrow_forwardChapter 5, Section 1, Exercise 009 The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution.Test H0 : p=0.55 vs Ha : p≠0.55 when the sample has n=70, and p^=0.38 with SE=0.06.Find the value of the standardized z-test statistic.Round your answer to two decimal places.z= Enter your answer in accordance to the question statementarrow_forward
- .A sample of 9 measurements, randomly selected from a normally distributed population, resulted in x= 2.6, and s= 0.9 Conduct a hypothesis test to verify the claim that the population mean is greater than 2.5 . Use a=.05arrow_forwardA kinesiologist claims that the resting heart rate of men aged 18 to 25 who exercise regularly is less than that of men who do not exercise regularly. Men in each category were selected at random and their resting heart rates were measured, with the following results: n Regular exercise 40 63 1.0 No regular exercise 30 71 1.2 (a) Set up the appropriate H0 and Ha. (b) Propose a formula to calculate the test statistic and report the result. (c) Find the P-value and make your conclusion on α = .05.arrow_forwardIf all other values are held constant, what happens to the value of t when sample size increases ?arrow_forward
- Chapter 6, Section 5, Exercise 232 Use a t-distribution to find a confidence interval for the difference in means μd=μ1-μ2 using the relevant sample results from paired data. Assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using d=x1-x2.A 95% confidence interval for μd using the paired difference sample results x¯d=1.4, sd=2.0, nd=30.Give the best estimate for μd, the margin of error, and the confidence interval.Enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places.Best estimate = Enter your answer; Best estimate.Margin of error = Enter your answer; Margin of error.The 95% confidence interval is Enter your answer; The 95% confidence interval, value 1 to Enter your answer; The 95% confidence interval, value 2.arrow_forwardIn Exercises 9–12, refer to the sample data from the given exercises in Section 13–2 on page 611. Use the Wilcoxon signed-ranks test for the claim about the median of a population. Exercise 14 “Earthquake Depths”arrow_forwardChapter 5, Section 1, Exercise 007 The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution.Test H0 : μ=85 vs Ha : μ>85 when the sample has n=19, x¯=82.2, and s=3.6 with SE=0.8.Find the value of the standardized z-test statistic.Round your answer to two decimal places.z= Enter your answer in accordance to the question statementarrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt