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According to the U.S. Bureau of Labor Statistics, 7.0%% of female hourly workers who are 16 to 24 years old are being paid minimum wage or less. (Note that some workers in some industries are exempt from the minimum wage requirement of the Fair Labor Standards Act and, thus, could be legally earning less than the "minimum" wage.) A prominent politician is interested in how young working women within her county compare to this national percentage, and selects a simple random sample of 500 female hourly workers who are 16 to 24 years old. Of the women in the sample, 42 are being paid minimum wage or less. From these sample results, and using the 0.10 level of significance, could the politician conclude that the percentage of young female hourly workers who are low-paid in her county might be the same as the percentage of young women who are low-paid in the nation as a whole? Determine and interpret the p-value for the test.Using the sample results in Exercise 10.71, construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized population proportion (0.07) within the interval? Given the presence or absence of the 0.07 value within the interval, is this consistent with the findings of the hypothesis test conducted in Exercise 10.71? Reference: Exercise 10.71 According to the U.S. Bureau of Labor Statistics, 7.0%% of female hourly workers who are 16 to 24 years old are being paid minimum wage or less. (Note that some workers in some industries are exempt from the minimum wage requirement of the Fair Labor Standards Act and, thus, could be legally earning less than the "minimum" wage.) A prominent politician is interested in how young working women within her county compare to this national percentage, and selects a simple random sample of 500 female hourly workers who are 16 to 24 years old. Of the women in the sample, 42 are being paid minimum wage or less. From these sample results, and using the 0.10 level of significance, could the politician conclude that the percentage of young female hourly workers who are low-paid in her county might be the same as the percentage of young women who are low-paid in the nation as a whole? Determine and interpret the p-value for the test.Brad Davenport, a consumer reporter for a national cable TV channel, is working on a story evaluating generic food products and comparing them to their brand-name counterparts. According to Brad, consumers claim to like the brand-name products better than the generics. but they can't even tell which is which. To test his theory, Brad gives each of 200 consumers two potato chips-one generic, the other a brand name-and asks them which one is the brand- name chip. Fifty-five percent of the subjects correctly identify the brand-name chip. At the 0.025 level, is this significantly greater than the 50%% that could be expected simply by chance? Determine and interpret the p-value for the test.It has been reported that 80% of taxpayers who are audited by the Internal Revenue Service end up paying more money in taxes. Assume that auditors are randomly assigned to cases, and that one of the ways the IRS oversees its auditors is to monitor the percentage of cases that result in the taxpayer paying more taxes. If a sample of 400 cases handled by an individual auditor has 77_0% of those she audited paying more taxes, is there reason to believe her overall "pay more" percentage might be some value other than 80%? Use the 0.10 level of significance in reaching a conclusion. Determine and interpret the p-value for the test.Based on the sample results in Exercise 10.74,construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized proportion (0.80) within the interval? Given the presence or absence of the 0.80 value within the interval, is this consistent with the findings of the hypothesis test conducted in Exercise 10.74? Reference: Exercise 10.74 It has been reported that 80%% of taxpayers who are audited by the Internal Revenue Service end up paying more money in taxes. Assume that auditors are randomly assigned to cases, and that one of the ways the IRS oversees its auditors is to monitor the percentage of cases that result in the taxpayer paying more taxes. If a sample of 400 cases handled by an individual auditor has 77.0% of those she audited paying more taxes, is there reason to believe her overall "pay more" percentage might be some value other than 80%? Use the 0.10 level of significance in reaching a conclusion. Determine and interpret the p-value for the test.( DATA SET ) Note: Exercises require a computer and statistical software. According to the National Collegiate Athletic Association (NCAA). 41% of male basketball players graduate within 6 years of enrolling in their college or university, compared to 50%% for the student body as a whole. Assume that data file XR10076 shows the current status for a sample of 200 male basketball players who enrolled in New England colleges and universities 0 years ago. The data codes are 1 = left school, 2 = still in school, 3 = graduated. Using these data and the 0.10 level of significance, does the graduation rate for male basketball players from schools in this region differ significantly from the 41%% for male basketball players across the nation? Identify and interpret the p-value for the test.( DATA SET ) Note: Exercises require a computer and statistical software. Using the sample results in Exercise 10.76, construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized proportion (0.41) within the interval? Given the presence or absence of the 0.41 value within the interval, is this consistent with the findings of the hypothesis test conducted in Exercise 10.78? Reference: Exercise 10.76 According to the National Collegiate Athletic Association (NCAA). 41%% of male basketball players graduate within 6 years of enrolling in their college or university, compared to 56%% for the student body as a whole. Assume that data file XR10076 shows the current status for a sample of 200 male basketball players who enrolled in New England colleges and universities 6 years ago. The data codes are 1 = left school, 2 = still in school, 3 = graduated. Using these data and the 0.10 level of significance, does the graduation rate for male basketball players from schools in this region differ significantly from the 41%% for male basketball players across the nation? Identify and interpret the p-value for the test.For the test described in Exercise 10.31, if the true population mean is really 2.520 inches, what is the probability that the inspector will correctly reject the false null hypothesis that u = 2 500 inches? Reference : Exercise 10.31 Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with a standard deviation of 0.027 inches. As the machine functions over an extended number of work shifts, the standard deviation remains unchanged, but the combination of accumulated deposits and mechanical wear causes the mean diameter to "drift" away from the desired 2.500 inches. For a recent random sample of 34 tubes, the mean diameter was 2.509 inches. At the 0.01 level of significance, does the machine appear to be in need of maintenance and calibration? Determine and interpret the p-value for the test.For the test described in Exercise 10.32, assume that the true population mean for the new booklet is u = 2.80 hours. Under this assumption, what is the probability that the false null hypothesis, Hip 2 3.00 hours, will be rejected? Reference : Exercise 10.32 A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 3 hours, with a standard deviation of 0.20 hours. A consultant has developed a new instructional booklet intended to reduce the time an inexperienced kit builder will need to assemble the device. In a test of the effectiveness of the new booklet, 15 novices require a mean of 2.90 hours to complete the job. Assuming the population of times is normally distributed, and using the 0.05 level of significance, should we conclude that the new booklet is effective? Determine and interpret the p-value for the test.Using assumed true population means of 2.80, 2.85, 2.90, 2 95, and 3.00 hours, plot the power curve for the test in Exercise 10.32. Reference : Exercise 10.32 A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 3 hours, with a standard deviation of 0.20 hours. A consultant has developed a new instructional booklet intended to reduce the time an inexperienced kit builder will need to assemble the device. In a test of the effectiveness of the new booklet, 15 novices require a mean of 2.90 hours to complete the job. Assuming the population of times is normally distributed, and using the 0.05 level of significance, should we conclude that the new booklet is effective? Determine and interpret the p-value for the test.The new director of a local YMCA has been told by his predecessors that the average member has belonged for 8.7 years. Examining a random sample of 15 membership files, he finds the mean length of of 2.5 years. Assuming the population is approximately normally distributed, and using the 0.05 level, does this result suggest that the actual mean length of membership to be 7.2 years, with a standard deviation membership may be some value other than 8.7 years?A scrap metal dealer claims that the mean of his cash sales is "no more than $80," but an Inter nal Revenue Service agent believes the dealer is untruthful. Observing a sample of 20 cash customers, the agent finds the mean purchase to be $91, with a standard deviation of $21. Assuming the population is approximately normally distributed, and using the 0.05 level of significance, is the agent's suspicion confirmed?Taxco, a firm specializing in the preparation of income tax returns, claims the mean refund for customers who received refunds last year was $150. For a random sample of 12 customers who received refunds last year, the mean amount was found to be $125, with a standard deviation of $43. Assuming that the population is approximately normally distributed, and using the 0.10 level in a two-tail test, do these results suggest that Taxco's assertion may be accurate?During 2008, college work-study students earned a mean of $1478. Assume that a sample consisting of 45 of the work-study students at a large university was found to have earned a mean of $1503 during that year, with a standard deviation of $210. Would a one-tail test at the 0.05 level suggest the average earnings of this university's work-study students were significantly higher than the national mean?According to the Federal Reserve Board, the mean net worth of U.S. households headed by persons 75 years or older is $840,000. Suppose a simple random sample of 50 households in this age group is obtained from a certain region of the United States and is found to have a mean net worth of $815,000, with a standard deviation of $120,000. From these sample results, and using the 0.05 level of significance in a two-tail test, comment on whether the mean net worth for all the region's households in this age category might not be the same as the mean value reported for their counterparts across the nation.It has been reported that the average life for halogen lightbulbs is 4000 hours. Learning of this figure, a plant manager would like to find out whether the vibration and temperature conditions that the facility's bulbs encounter might be having an adverse effect on the service life of bulbs in her plant. In a test involving 15 halogen bulbs installed in various locations around the plant, she finds the average life for bulbs in the sample is 3882 hours, with a standard deviation of 200 hours. Assuming the population of halogen bulb lifetimes to be approximately normally distributed, and using the 0.025 level of significance, do the test results tend to support the manager's suspicion that adverse conditions might be detrimental to the operating lifespan of halogen lightbulbs used in her plant?In response to an inquiry from its national office, the manager of a local bank has stated that her bank's average service time for a drive-through customer is 93 seconds. A student intern working at the bank happens to be taking a statistics course and is curious as to whether the true average might be some value other than 93 seconds. The intern observes a simple random sample of 50 drive-through customers whose average service time is 89.5 seconds, with a standard deviation of 11.3 seconds. From these sample results, and using the 0.05 level of significance, what conclusion would the student reach with regard to the bank manager's claim?Using the sample results in Exercise 10.52, construct and interpret the 95% confidence interval for the population mean. Is the hypothesized population mean (93 seconds) within the interval? Given the presence or absence of the 93 seconds value within the interval, is this consistent with the findings of the hypothesis test conducted in Exercise 10.52? Reference: Exercise 10.52 In response to an inquiry from its national office, the manager of a local bank has stated that her bank's average service time for a drive-through customer is 93 seconds. A student intern working at the bank happens to be taking a statistics course and is curious as to whether the true average might be some value other than 93 seconds. The intern observes a simple random sample of 50 drive-through customers whose average service time is 89.5 seconds, with a standard deviation of 11.3 seconds. From these sample results, and using the 0.05 level of significance, what conclusion would the student reach with regard to the bank manager's claim?The U.S. Census Bureau says the 52-question "long form" received by 1 in 3 households during the 2000 census takes a mean of 38 minutes to complete. Suppose a simple random sample of 35 persons is given the form, and their mean time to complete it is 36.8 minutes, with a standard deviation of 4.0 minutes. From these sample results, and using the 0.10 level of significance, would it seem that the actual population mean time for completion might be some value other than 38 minutes?Using the sample results in Exercise 10.54, construct and interpret the 90% confidence interval for the population mean. Is the hypothesized population mean (38 minutes) within the interval? Given the presence or absence of the 38 minutes value within the interval, is this consistent with the findings of the hypothesis test conducted in Exercise 10.54? Reference: Exercise 10.54 The U.S. Census Bureau says the 52-question "long form" received by 1 in 8 households during the 2000 census takes a mean of 38 minutes to complete. Suppose a simple random sample of 35 persons is given the form, and their mean time to complete it is 36.8 minutes, with a standard deviation of 4.0 minutes. From these sample results, and using the 0.10 level of significance, would it seem that the actual population mean time for completion might be some value other than 38 minutes
