OIS Stats Final Ch. 8-9
The cost of a college education has increased at a much faster rate than costs in general over the past twenty years. In order to compensate for this, many students work part- or full-time in addition to attending classes. At one university, it is believed that the average hours students work per week exceeds 20. To test this at a significance level of 0.05, a random sample of n = 20 students was selected and the following values were observed: 26 15 10 40 10 20 30 36 40 0 5 10 20 32 16 12 40 36 10 0 Based on these sample data, the critical value expressed in hours: is approximately equal to 25.0 hours. is approximately equal to 25.26 hours. is approximately 22 hours. cannot be determined without knowing the population standard deviation.
is approximately equal to 25.26 hours.
If the p value is less than α in a two-tailed test, a one-tailed test should be used. the null hypothesis should not be rejected. the null hypothesis should be rejected. More information is needed to reach a conclusion about the null hypothesis.
the null hypothesis should be rejected.
For the following hypothesis test: H0 : u ≤ 45 Ha : u > 45 With n = 80, σ = 9, and = 47.1, state the calculated value of the test statistic z. 3.151 -3.121 -2.141 2.087
2.087
According to USA Today, customers are not settling for automobiles straight off the production lines. As an example, those who purchase a $355,000 Rolls-Royce typically add $25,000 in accessories. One of the affordable automobiles to receive additions is BMW's Mini Cooper. A sample of 179 recent Mini purchasers yielded a sample mean of $5,000 above the $20,200 base sticker price. Suppose the cost of accessories purchased for all Mini Coopers has a standard deviation of $1,500. Determine the margin of error in estimating the average cost of accessories on Mini Coopers. 219.75 291.11 231.14 214.41
219.75
A production process that fills 12-ounce cereal boxes is known to have a population standard deviation of 0.009 ounce. If a consumer protection agency would like to estimate the mean fill, in ounces, for 12-ounce cereal boxes with a confidence level of 92% and a margin of error of 0.001, what size sample must be used? 211 512 249 351
249
At issue is the proportion of people in a particular county who do not have health care insurance coverage. A simple random sample of 240 people was asked if they have insurance coverage, and 66 replied that they did not have coverage. Based on these sample data, determine the 95% confidence interval estimate for the population proportion. (0.239, 0.321) (0.224, 0.336) (0.259, 0.301) (0.268, 0.292)
(0.224, 0.336)
As the automobile accident rate increases, insurers are forced to increase their premium rates. Companies such as Allstate have recently been running a campaign they hope will result in fewer accidents by their policyholders. For each six-month period that a customer goes without an accident, Allstate will reduce the customer's premium rate by a certain percentage. Companies like Allstate have reason to be concerned about driving habits, based on a survey conducted by Drive for Life, a safety group sponsored by Volvo of North America, in which 1,100 drivers were surveyed. Among those surveyed, 74% said that careless or aggressive driving was the biggest threat on the road. One-third of the respondents said that cell phone usage by other drivers was the driving behavior that annoyed them the most. Based on these data, assuming that the sample was a simple random sample, construct and interpret a 95% confidence interval estimate for the true proportion in the population of all drivers who are annoyed by cell phone users. (0.316, 0.344) (0.313, 0.347) (0.306, 0.354) (0.302, 0.358)
(0.302, 0.358)
Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of 1,000 passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the 1,000 passengers, 345 had more than one bag. Based on this sample, develop and interpret a 95% confidence interval estimate for the proportion of the traveling population that would have been impacted had the one-bag limit been in effect. (0.3336, 0.3564) (0.3216, 0.3684) (0.3220, 0.3680) (0.3155, 0.3745)
(0.3155, 0.3745)
A survey of 499 women for the American Orthopedic Foot and Ankle Society revealed that 38% wear flats to work. Use this sample information to develop a 99% confidence interval for the population proportion of women who wear flats to work. 0.363, 0.397) (0.368, 0.392) (0.324, 0.436) (0.302, 0.458)
(0.324, 0.436)
Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of 1,000 passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the 1,000 passengers, 345 had more than one bag. Suppose the airline also noted whether the passenger was male or female. Out of the 1,000 passengers observed, 690 were males. Of this group, 280 had more than one bag. Using this data, obtain and interpret a 95% confidence interval estimate for the proportion of male passengers in the population who would have been affected by the one-bag limit. (0.3814, 0.4125) (0.3692, 0.4424) (0.2815, 0.5124) (0.3361, 0.4712)
(0.3692, 0.4424)
A decision maker is interested in estimating a population proportion. A sample of size n = 150 yields 115 successes. Based on these sample data, construct a 90% confidence interval estimate for the true population proportion. (0.747, 0.846) (0.737, 0.803) (0.714, 0.826) (0.750, 0.790)
(0.714, 0.826)
Construct a 98% confidence interval estimate for the population mean given the following values: (113.13, 126.87) (113.67, 126.33) (117.46, 122.54) (113.41, 126.59)
(113.41, 126.59)
Suppose a study of 196 randomly sampled privately insured adults with incomes over 200% of the current poverty level is to be used to measure out-of-pocket medical expenses for prescription drugs for this income class. The sample data are in the file Drug Expenses. Based on the sample data, construct a 95% confidence interval estimate for the mean annual out-of-pocket expenditures on prescription drugs for this income class. Interpret this interval. (161.97, 173.07) (162.08, 172.96) (163.50, 171.54) (164.19, 170.85)
(163.50, 171.54)
Even before the record gas prices during the summer of 2008, an article written by Will Lester of the Associated Press reported on a poll in which 80% of those surveyed say that Americans who currently own a SUV (sport utility vehicle) should switch to a more fuel-efficient vehicle to ease America's dependency on foreign oil. This study was conducted by the Pew Research Center for the People & the Press. As a follow-up to this report, a consumer group conducted a study of SUV owners to estimate the mean mileage for their vehicles. A simple random sample of 91 SUV owners was selected, and the owners were asked to report their highway mileage. The following results were summarized from the sample data: = 18.2 mpg s = 6.3 mpg Based on these sample data, compute and interpret a 90% confidence interval estimate for the mean highway mileage for SUVs. (17.1, 19.3) (17.6, 18.8) (15.4, 21.0) (12.4, 24.0)
(17.1, 19.3)
Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of 1,000 passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the 1,000 passengers, 345 had more than one bag. The domestic version of Boeing's 747 has a capacity for 568 passengers. Determine an interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane. Assume the plane is at its passenger capacity. (171.651, 216.214) (181.514, 208.313) (174.412, 217.218) (179.20, 212.716)
(179.20, 212.716)
According to USA Today, customers are not settling for automobiles straight off the production lines. As an example, those who purchase a $355,000 Rolls-Royce typically add $25,000 in accessories. One of the affordable automobiles to receive additions is BMW's Mini Cooper. A sample of 179 recent Mini purchasers yielded a sample mean of $5,000 above the $20,200 base sticker price. Suppose the cost of accessories purchased for all Mini Coopers has a standard deviation of $1,500. Calculate a 95% confidence interval for the average cost of accessories on Mini Coopers. (4850.33, 5149.67) (4878.82, 5121.18) (4780.25, 5219.75) (4788.86, 5211.14)
(4780.25, 5219.75)
The file Danish Coffee contains a random sample of 144 Danish coffee drinkers and measures the annual coffee consumption in kilograms for each sampled coffee drinker. A marketing research firm wants to use this information to develop an advertising campaign to increase Danish coffee consumption. Develop and interpret a 90% confidence interval estimate for the mean annual coffee consumption of Danish coffee drinkers. (6.4257, 6.6479) (6.3881, 6.6855) (6.3366, 6.7370) (6.1768, 6.8968)
(6.3881, 6.6855)
The U.S. Bureau of Labor Statistics (www.bls.gov) released its Consumer Expenditures report in October 2008. Among its findings is that average annual household spending on food at home was $3,624. Suppose a random sample of 137 households in Detroit was taken to determine whether the average annual expenditure on food at home was less for consumer units in Detroit than in the nation as a whole. The sample results are in the file Detroit Eats. Based on the sample results, can it be concluded at the α = 0.02 level of significance that average consumer-unit spending for food at home in Detroit is less than the national average? Because t = -15.7648 is less than the critical t value of -2.0736, do not reject H0. The annual average consumer unit spending for food at home in Detroit is not less than the 2006 national consumer unit average. Because t = -15.7648 is less than the critical t value of -2.0736, reject H0. The annual average consumer unit spending for food at home in Detroit is less than the 2006 national consumer unit average. Because t = -13.2314 is less than the critical t value of -1.4126, reject H0. The annual average consumer unit spending for food at home in Detroit is less than the 2006 national consumer unit average Because t = -13.2314 is less than the critical t value of -1.4126, do not reject H0. The annual average consumer unit spending for food at home in Detroit is not less than the 2006 national consumer unit average
-2.0736, reject H0. The annual average consumer unit spending for food at home in Detroit is less than the 2006 national consumer unit average.
For the following z-test statistic, compute the p-value assuming that the hypothesis test is a one-tailed test: z = 2.09. 0.0172 0.0183 0.0611 0.0415
0.0183
The produce manager for a large retail food chain is interested in estimating the percentage of potatoes that arrive on a shipment with bruises. A random sample of 150 potatoes showed 14 with bruises. Based on this information, what is the margin of error for a 95 percent confidence interval estimate? 0.0466 0.0006 0.0933 Can't be determined without knowing σ.
0.0466
According to data from the Environmental Protection Agency, the average daily water consumption for a household of four people in the United States is approximately at least 243 gallons. (Source: http://www.catskillcenter.org/programs/csp/H20/Lesson3/house3.htm) Suppose a state agency plans to test this claim using an alpha level equal to 0.05 and a random sample of 100 households with four people. Calculate the probability of committing a Type II error if the true population mean is 230 gallons. Assume that the population standard deviation is known to be 40 gallons. 0.1412 0.0331 0.0537 0.0712
0.0537
For the following z-test statistic, compute the p-value assuming that the hypothesis test is a one-tailed test: z = -1.55. 0.0172 0.0901 0.1512 0.0606
0.0606
Waiters at Finegold's Restaurant and Lounge earn most of their income from tips. Each waiter is required to "tip-out" a portion of tips to the table bussers and hostesses. The manager has based the "tip-out" rate on the assumption that the mean tip is at least 15% of the customer bill. To make sure that this is the correct assumption, he has decided to conduct a test by randomly sampling 60 bills and recording the actual tips. Calculate the probability of a Type II error if the true mean is 14%. Assume that the population standard deviation is known to be 2% and that a significance level equal to 0.01 will be used to conduct the hypothesis test. 0.0606 0.0041 0.4123 0.1251
0.0606
For the following z-test statistic, compute the p-value assuming that the hypothesis test is a one-tailed test: z = 1.34. 0.0124 0.0815 0.0606 0.0901
0.0901
According to CNN business partner Careerbuilder.com, the average starting salary for accounting graduates in 2008 was at least $47,413. Suppose that the American Society for Certified Public Accountants planned to test this claim by randomly sampling 200 accountants who graduated in 2008. Compute the power of the hypothesis test to reject the null hypothesis if the true average starting salary is only $47,000. Assume that the population standard deviation is known to be $4,600 and the test is to be conducted using an alpha level equal to 0.01. 0.8554 0.0872 0.9812 0.1446
0.8554
A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, how large could the sample mean be before they would reject the null hypothesis? 16.2 ounces 15.8 ounces 16.049 ounces 16.041 ounces
16.041 ounces
A pilot sample of 75 items was taken, and the number of items with the attribute of interest was found to be 15. How many more items must be sampled to construct a 99% confidence interval estimate for p with a 0.025 margin of error? 1512 1623 1612 1698
1623
Woof Chow Dog Food Company believes that it has a market share of 25 percent. It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food, and 23 people say yes. Based upon this information, what is the critical value if the hypothesis is to be tested at the 0.05 level of significance? 1.28 1.96 2.575 1.645
1.96
Suppose an airline decides to conduct a survey of its customers to determine their opinion of a proposed one-bag limit. The plan calls for a random sample of customers on different flights to be given a short written survey to complete during the flight. One key question on the survey will be: "Do you approve of limiting the number of carry-on bags to a maximum of one bag?" Airline managers expect that only about 15% will say "yes." Based on this assumption, what size sample should the airline take if it wants to develop a 95% confidence interval estimate for the population proportion who will say "yes" with a margin of error of ±0.02? 1151 1512 1341 1225
1225
An advertising company wishes to estimate the mean household income for all single working professionals who own a foreign automobile. If the advertising company wants a 90% confidence interval estimate with a margin of error of ±$2,500, what sample size is needed if the population standard deviation is known to be $27,500? 328 156 251 415
328
Suppose a study estimated the population mean for a variable of interest using a 99% confidence interval. If the width of the estimated confidence interval (the difference between the upper limit and the lower limit) is 600 and the sample size used in estimating the mean is 1,000, what is the population standard deviation? 3684.21 2451.23 26711.14 5125.11
3684.21
A public policy research group is conducting a study of health care plans and would like to estimate the average dollars contributed annually to health savings accounts by participating employees. A pilot study conducted a few months earlier indicated that the standard deviation of annual contributions to such plans was $1,225. The research group wants the study's findings to be within $100 of the true mean with a confidence level of 90%. What sample size is required? 546 361 407 512
407
The file Danish Coffee contains a random sample of 144 Danish coffee drinkers and measures the annual coffee consumption in kilograms for each sampled coffee drinker. A marketing research firm wants to use this information to develop an advertising campaign to increase Danish coffee consumption. Based on the sample's results, what is the best point estimate of average annual coffee consumption for Danish coffee drinkers? 6.5368 6.1411 7.4127 7.4151
6.5368
A manager wishes to estimate a population mean using a 95% confidence interval estimate that has a margin of error of ±44.0. If the population standard deviation is thought to be 680, what is the required sample size? 1215 918 1050 871
918
A cell phone service provider has selected a random sample of 20 of its customers in an effort to estimate the mean number of minutes used per day. The results of the sample included a sample mean of 34.5 minutes and a sample standard deviation equal to 11.5 minutes. Based on this information, and using a 95 percent confidence level: the critical value is t = 2.093 the critical value is z = 1.645 the critical value is z = 1.96 The critical value can't be determined without knowing the margin of error.
?
A hypothesis test is to be conducted using an alpha = .05 level. This means: there is a maximum 5 percent chance that a true null hypothesis will be rejected. there is a 5 percent chance that the null hypothesis is true. there is a 5 percent chance that a Type II error has been committed. there is a 5 percent chance that the alternative hypothesis is true.
?
Allante Pizza delivers pizzas throughout its local market area at no charge to the customer. However, customers often tip the driver. The owner is interested in estimating the mean tip income per delivery. To do this, she has selected a simple random sample of 12 deliveries and has recorded the tips that were received by the drivers. These data are: $2.25 $2.50 $2.25 $2.00 $2.00 $1.50 $0.00 $2.00 $1.50 $2.00 $3.00 $1.50 Based on these sample data, what is the best point estimate to use as an estimate of the true mean tip per delivery? 1.811 1.875 1.50 1.312
?
The U.S. Post Office is interested in estimating the mean weight of packages shipped using the overnight service. They plan to sample 300 packages. A pilot sample taken last year showed that the standard deviation in weight was about 0.15 pound. If they are interested in an estimate that has 95 percent confidence, what margin of error can they expect? About 0.0003 pound Approximately 0.017 pound About 1.96 Can't be determined without knowing the population mean.
Approximately 0.017 pound
Suppose that an internal report submitted to the managers at a bank in Boston showed that with 95 percent confidence, the proportion of the bank's customers who also have accounts at one or more other banks is between .45 and .51. Given this information, what sample size was used to arrive at this estimate? About 344 Just under 700 Approximately 1,066 Can't be determined without more information.
Approximately 1,066
A study has indicated that the sample size necessary to estimate the average electricity use by residential customers of a large western utility company is 900 customers. Assuming that the margin of error associated with the estimate will be ±30 watts and the confidence level is stated to be 90 percent, what was the value for the population standard deviation? 265 watts About 490 watts Approximately 547.1 watts Can't be determined without knowing the size of the population.
Approximately 547.1 watts
A sample of 250 people resulted in a confidence interval estimate for the proportion of people who believe that the federal government's proposed tax increase is justified is between 0.14 and 0.20. Based on this information, what was the confidence level used in this estimation? Approximately 79 percent 95 percent Approximately 1.59 Can't be determined without knowing σ.
Approximately 79 percent
A hospital emergency room has collected a sample of n = 40 to estimate the mean number of visits per day. It has found the standard deviation is 32. Using a 90 percent confidence level, what is its margin of error? Approximately ±8.3 visits Approximately ±1.5 visits About ±1.3 visits About ±9.9 visits
Approximately ±8.3 visits
A contract calls for the mean diameter of a cylinder to be 1.50 inches. As a quality check, each day a random sample of n = 36 cylinders is selected and the diameters are measured. Assuming that the population standard deviation is thought to be 0.10 inch and that the test will be conducted using an alpha equal to 0.025, what would the probability of a Type II error be? Can't be determined without knowing the "true" population mean. Approximately 0.1267 0.975 About 0.6789
Can't be determined without knowing the "true" population mean.
Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures and share little in common with each other. True False
False
Generally, it is possible to appropriately test a null and alternative hypotheses using the test statistic approach and reach a different conclusion than would be reached if the p-value approach were used. True False
False
A large tire manufacturing company has claimed that its top line tire will average more than 80,000 miles. If a consumer group wished to test this claim, they would formulate the following null and alternative hypotheses: H0 : μ ≥ 80,000 Hα : μ ≠ 80,000 True False
False
A local medical center has advertised that the mean wait for services will be less than 15 minutes. In an effort to test whether this claim can be substantiated, a random sample of 100 customers was selected and their wait times were recorded. The mean wait time was 17.0 minutes. Based on this sample result, there is sufficient evidence to reject the medical center's claim. True False
False
A report recently submitted to the managing partner for a market research company stated "the hypothesis test may have resulted in either a Type I or a Type II error. We won't know which one occurred until later." This statement is one that we might correctly make for any hypothesis that we have conducted. True False
False
A two-tailed hypothesis test is used when the null hypothesis looks like the following: H0 : = 100. True False
False
All other factors held constant, the higher the confidence level, the closer the point estimate for the population mean will be to the true population mean. True False
False
Choosing an alpha of 0.01 will cause beta to equal 0.99. True False
False
If a hypothesis test is conducted for a population mean, a null and alternative hypothesis of the form: H0 : μ = 100 HA : μ ≠ 100 will result in a one-tailed hypothesis test since the sample result can fall in only one tail. True False
False
If a hypothesis test leads to incorrectly rejecting the null hypothesis, a Type II statistical error has been made. True False
False
If the sample data lead the decision maker to reject the null hypothesis, the alpha level is the maximum probability of committing a Type II error. True False
False
In a hypothesis test, the p-value measures the probability that the alternative hypothesis is true. True False
False
In a one-tailed hypothesis test, the larger the significance level, the greater the critical value will be. True False
False
In a two-tailed hypothesis test the area in each tail of the rejection region is equal to α. True False
False
The Adams Shoe Company believes that the mean size for men's shoes is now more than 10 inches. To test this, it has selected a random sample of n = 100 men. Assuming that the test is to be conducted using a .05 level of significance, a p-value of .07 would lead the company to conclude that its belief is correct. True False
False
The critical value in a null hypothesis test is called alpha. True False
False
The executive director of the United Way believes that more than 24 percent of the employees in the high-tech industry have made voluntary contributions to the United Way. In order to test this statistically, the appropriate null and alternative hypotheses are: H0 : ≤ .24 HA : > .24 True False
False
The following is an appropriate statement of the null and alternate hypotheses for a test of a population mean: H0 : μ 50 HA : μ > 50 True False
False
The following is an appropriate statement of the null and alternate hypotheses for a test of a population mean: H0: μ < 50 HA : μ > 50 True False
False
The impact on the margin of error for a confidence interval for an increase in confidence level and a decrease in sample size is unknown since these changes are contradictory. True False
False
The police chief in a local city claims that the average speed for cars and trucks on a stretch of road near a school is at least 45 mph. If this claim is to be tested, the null and alternative hypotheses are: H0 : μ 45 mph Ha : μ ≥ 45 mph True False
False
The state insurance commissioner believes that the mean automobile insurance claim filed in her state exceeds $1,700. To test this claim, the agency has selected a random sample of 20 claims and found a sample mean equal to $1,733 and a sample standard deviation equal to $400. They plan to conduct the test using a 0.05 significance level. Given this, the appropriate null and alternative hypotheses are H0 : ≤ $1,700 HA : > $1,700 True False
False
When someone has been accused of a crime the null hypothesis is: H0 : innocent. In this case, a Type I error would be convicting an innocent person. True False
False
When using the p-value method, the null hypothesis is rejected when the calculated p-value > α. True False
False
A major issue facing many states is whether to legalize casino gambling. Suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling. However, before backing a proposal to allow such gambling, the governor has instructed his aides to conduct a statistical test on the issue. To do this, the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state. Of these 300 voters, 175 actually favored legalized gambling. State the appropriate null and alternative hypotheses. H0 : p ≤ 0.58 Ha : p > 0.58 H0 : p = 0.58 Ha : p ≠ 0.58 H0 : p ≤ 0.55 Ha : p > 0.55 H0 : p = 0.55 Ha : p ≠ 0.55
H0 : p ≤ 0.55 Ha : p > 0.55
The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces. Every box of cereal is not expected to contain exactly the targeted weight, but the average of all boxes filled should. At the end of every shift (eight hours), 16 boxes are selected at random and the mean and standard deviation of the sample are computed. Based on these sample results, the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate. Use α = 0.05. Establish the appropriate null and alternative hypotheses to be tested for boxes that are supposed to have an average of 24 ounces. H0 : μ = 22 ounces Ha : μ ≠ 22 ounces H0 : μ = 16 ounces Ha : μ ≠ 16 ounces H0 : μ = 32 ounces Ha : μ ≠ 32 ounces H0 : μ = 24 ounces Ha : μ ≠ 24 ounces
H0 : μ = 24 ounces Ha : μ ≠ 24 ounces
According to CNN business partner Careerbuilder.com, the average starting salary for accounting graduates in 2008 was at least $47,413. Suppose that the American Society for Certified Public Accountants planned to test this claim by randomly sampling 200 accountants who graduated in 2008. State the appropriate null and alternative hypotheses. H0 : μ ≤ $47,413 HA : μ > $47,413 H0 : μ < $47,413 HA : μ ≥ $47,413 H0 : μ > $47,413 HA : μ ≤ $47,413 H0 : μ ≥ $47,413 HA : μ < $47,413
H0 : μ ≥ $47,413 HA : μ < $47,413
Waiters at Finegold's Restaurant and Lounge earn most of their income from tips. Each waiter is required to "tip-out" a portion of tips to the table bussers and hostesses. The manager has based the "tip-out" rate on the assumption that the mean tip is at least 15% of the customer bill. To make sure that this is the correct assumption, he has decided to conduct a test by randomly sampling 60 bills and recording the actual tips. State the appropriate null and alternative hypotheses. H0 : μ ≥ 9 Ha : μ < 9 H0 : μ ≤ 9 Ha : μ > 9 H0 : μ ≥ 15 Ha : μ < 15 H0 : μ ≤ 15 Ha : μ > 15
H0 : μ ≥ 15 Ha : μ < 15
The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces. Every box of cereal is not expected to contain exactly the targeted weight, but the average of all boxes filled should. At the end of every shift (eight hours), 16 boxes are selected at random and the mean and standard deviation of the sample are computed. Based on these sample results, the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate. At the end of a particular shift during which the machine was filling 24-ounce boxes of Mini-Oats, the sample mean of 16 boxes was 24.32 ounces, with a standard deviation of 0.70 ounce. Assist the production control manager in determining if the machine is achieving its targeted average at alpha = 0.05. Process is not running okay; therefore reject H0 Process is running okay, reject the Ho: Process is running okay, do not reject H0 Process is not running okay, reject the Ho:
Process is running okay, do not reject H0
A company that sells an online course aimed at helping high-school students improve their SAT scores has claimed that SAT scores will improve by more than 90 points on average if students successfully complete the course. To test this, a national school counseling organization plans to select a random sample of n = 100 students who have previously taken the SAT test. These students will take the company's course and then retake the SAT test. Assuming that the population standard deviation for improvement in test scores is thought to be 30 points and the level of significance for the hypothesis test is 0.05, find the critical value in terms of improvement in SAT points, which would be needed prior to finding a beta. Reject the null if SAT improvement is > 95 points. Reject the null if SAT improvement is > 94.935 points. Reject the null if SAT improvement is > 95.88 points. Reject the null if SAT improvement is 85.065 points.
Reject the null if SAT improvement is > 94.935 points.
A mail-order business prides itself in its ability to fill customers' orders in six calendar days or less on the average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. Based on this sample information, he decides if the desired standard is not being met. He will assume that the average number of days to fill customers' orders is six or less unless the data suggest strongly otherwise. On one occasion where a sample of 40 customers was selected, the average number of days was 6.65, with a sample standard deviation of 1.5 days. Can the operations manager conclude that his mail-order business is achieving its goal? Use a significance level of 0.025 to answer this question. Since 2.7406 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal. Since 2.4421 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal. Since 2.2346 < 2.5113, reject H0 and conclude that the mail-order business is not achieving its goal. Since 2.2216 < 2.4511, reject H0 and conclude that the mail-order business is not achieving its goal
Since 2.7406 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal.
Hono Golf is a manufacturer of golf products in Taiwan and China. One of the golf accessories it produces at its plant in Tainan Hsing, Taiwan, is plastic golf tees. The injector molder produces golf tees that are designed to have an average height of 66 mm. To determine if this specification is met, random samples are taken from the production floor. One sample is contained in the file labeled THeight. Determine if the process is not producing the tees to specification. Use a significance level of 0.01. Since t = 1.2814 < 1.9211 reject H0. There is sufficient evidence to conclude that the average height of the plastic tees is different from 66 mm. Since t = 2.1953 < 2.8073 reject H0. There is sufficient evidence to conclude that the average height of the plastic tees is different from 66 mm. Since t = 2.1953 < 2.8073 do not reject H0. There is not sufficient evidence to conclude that the average height of the plastic tees is different from 66 mm. Since t = 1.2814 < 1.9211 do not reject H0. There is not sufficient evidence to conclude that the average height of the plastic tees is different from 66 mm.
Since t = 2.1953 < 2.8073 do not reject H0. There is not sufficient evidence to conclude that the average height of the plastic tees is different from 66 mm.
A major issue facing many states is whether to legalize casino gambling. Suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling. However, before backing a proposal to allow such gambling, the governor has instructed his aides to conduct a statistical test on the issue. To do this, the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state. Of these 300 voters, 175 actually favored legalized gambling. Assuming that a significance level of 0.05 is used, what conclusion should the governor reach based on these sample data? Since z = 1.1594 < 1.645, do not reject the null hypothesis. The sample data do not provide sufficient evidence to conclude that more than 55 percent of the population favor legalized gambling. Since z = 2.1316 > 1.645, reject the null hypothesis. The sample data provide sufficient evidence to conclude that more than 58 percent of the population favor legalized gambling. Since z = 2.1316 > 1.645, reject the null hypothesis. The sample data provide sufficient evidence to conclude that more than 55 percent of the population favor legalized gambling. Since z = 1.1594 < 1.645, do not reject the null hypothesis. The sample data do not provide sufficient evidence to conclude that more than 58 percent of the population favor legalized gambling.
Since z = 1.1594 < 1.645, do not reject the null hypothesis. The sample data do not provide sufficient evidence to conclude that more than 55 percent of the population favor legalized gambling.
Which of the following statements is true? Alpha and beta are directly related such that when one is increased the other will increase also. The alternative hypothesis should contain the equality. The decision maker controls the probability of making a Type I statistical error. Alpha represents the probability of making a Type II error.
The decision maker controls the probability of making a Type I statistical error.
A local medical center has advertised that the mean wait for services will be less than 15 minutes. Given this claim, the hypothesis test for the population mean should be a one-tailed test with the rejection region in the lower (left-hand) tail of the sampling distribution. True False
True
A report recently published in a major business periodical stated that the average salary for female managers is less than $50,000. If we were interested in testing this, the following null and alternative hypotheses would be established: H0 : μ ≥ 50,000 Hα : μ 50,000 True False
True
A two-tailed hypothesis test with α = 0.05 is similar to a 95 percent confidence interval. True False
True
In conducting a hypothesis test where the conclusion is to reject the null hypothesis, then either a correct decision has been made or else a Type I error. True False
True
In hypothesis testing, the null hypothesis should contain the equality sign. True False
True
Lube-Tech is a major chain whose primary business is performing lube and oil changes for passenger vehicles. The national operations manager has stated in an industry newsletter that the mean number of miles between oil changes for all passenger cars exceeds 4,200 miles. To test this, an industry group has selected a random sample of 100 vehicles that have come into a lube shop and determined the number of miles since the last oil change and lube. The sample mean was 4,278 and the sample standard deviation was 780 miles. Based on this information, the test statistic is approximately t = 1.000. True False
True
Of the two types of statistical errors, the one that decision makers have most control over is Type I error. True False
True
The loan manager for State Bank and Trust has claimed that the mean loan balance on outstanding loans at the bank is over $14,500. To test this at a significance level of 0.05, a random sample of n = 100 loan accounts is selected. Assuming that the population standard deviation is known to be $3,000, the null and alternative hypotheses to be tested are: H0 : μ ≤ $14,500 HA : μ > $14,500 True False
True
The loan manager for State Bank and Trust has claimed that the mean loan balance on outstanding loans at the bank is over $14,500. To test this at a significance level of 0.05, a random sample of n = 100 loan accounts is selected. Assuming that the population standard deviation is known to be $3,000, the value of that corresponds to the critical value is approximately $14,993.50. True False
True
The makers of weight loss product are interested in estimating the mean weight loss for users of their product. To do this, they have selected a random sample of n = 9 people and have provided them with a supply of the product. After six months, the nine people had an average weight loss of 15.3 pounds with a standard deviation equal to 3.5 pounds. The upper limit for the 90 percent confidence interval estimate for the population mean is approximately 17.47 pounds. True False
True
The null and alternate hypotheses must be opposites of each other. True False
True
The significance level in a hypothesis test corresponds to the maximum probability that a Type I error will be committed. True False
True
To calculate beta requires making a "what if" assumption about the true population parameter, where the "what-if" value is one that would cause the null hypothesis to be false. True False
True
Type II error is failing to reject the null hypothesis when the null is actually false. True False
True
When a battery company claims that their batteries last longer than 100 hours and a consumer group wants to test this claim, the hypotheses should be: H0 : μ ≤ 100 HA : μ > 100 True False
True
When deciding the null and alternative hypotheses, the rule of thumb is that if the claim contains the equality (e.g., at least, at most, no different from, etc.), the claim becomes the null hypothesis. If the claim does not contain the equality (e.g., less than, more than, different from), the claim is the alternative hypothesis. True False
True
When the decision maker has control over the null and alternative hypotheses, the alternative hypotheses should be the "research" hypothesis. True False
True
When using the p-value method for a two-tailed hypothesis, the p-value is found by finding the area in the tail beyond the test statistic, then doubling it. True False
True
When someone is on trial for suspicion of committing a crime, the hypotheses are: H0 : innocent HA : guilty Which of the following is correct? Type II error is convicting an innocent person. Type I error is convicting an innocent person. Type I error is acquitting a guilty person. Type II error is acquitting an innocent person.
Type I error is convicting an innocent person.
When someone is on trial for suspicion of committing a crime, the hypotheses are: H0 : innocent HA : guilty Which of the following is correct? Type II error is convicting an innocent person. Type II error is acquitting an innocent person. Type I error is acquitting a guilty person. Type I error is convicting an innocent person.
Type I error is convicting an innocent person.
The power of a test is measured by its capability of: rejecting a null hypothesis that is true. not rejecting a null hypothesis that is false. not rejecting a null hypothesis that is true. rejecting a null hypothesis that is false.
rejecting a null hypothesis that is false.
The manager of an online shop wants to determine whether the mean length of calling time of its customers is significantly more than 3 minutes. A random sample of 100 customers was taken. The average length of calling time in the sample was 3.1 minutes with a standard deviation of 0.5 minutes. At a 0.05 level of significance, it can be concluded that the mean of the population is: significantly less than 3. significantly greater than 3. not significantly greater than 3. not significantly different from 3.10.
significantly greater than 3.
Allante Pizza delivers pizzas throughout its local market area at no charge to the customer. However, customers often tip the driver. The owner is interested in estimating the mean tip income per delivery. To do this, she has selected a simple random sample of 12 deliveries and has recorded the tips that were received by the drivers. These data are: $2.25 $2.50 $2.25 $2.00 $2.00 $1.50 $0.00 $2.00 $1.50 $2.00 $3.00 $1.50 Suppose the owner is interested in developing a 90% confidence interval estimate. Given the fact that the population standard deviation is unknown, what distribution will be used to obtain the critical value? z-distribution t-distribution k-distribution s-distribution
t-distribution