Stat Possible Test Questions

A consumer agency is interested in examining whether there is a difference in two common sealant products used to waterproof residential backyard decks. With cooperation of several builders in the area, they randomly assign 38 newly constructed decks to be treated with Very Clear deck sealant and another 37 newly constructed decks to be treated with Sure Seal deck sealant. After one year of being exposed to similar weather conditions, the decks are rated on a scale of 1 to 100. The mean rating for the decks treated with Very Clear is 89.2 with a standard deviation of 3.1. The mean rating for the decks treated with Sure Seal is 92.4 with a standard deviation of 3.8. Which of the following represents the 90 percent confidence interval to estimate the difference (Very Clear minus Sure Seal) in mean ratings for the two deck sealants? not taking the time to type these long ass answers sorry

(89.2-92.4) ± 1.688 √3.1^2/38+ 3.8^2/37

Select all that apply. A person is testing whether a coin that a magician uses is biased. After analyzing the results from his coin flipping, the p value ends up being .21, so he concludes that there is no evidence that the coin is biased. Based on this information, which of these is/are possible 95% confidence intervals on the population proportion of times heads comes up? (.43, .55) (.32, .46) (.48, .64) (.76, .98) (.81, 1.33)

1 and 3

Select all that apply. Which of these 95% confidence intervals for the difference between means represent a significant different at the .05 level? (-4.6, -1.8) (-0.2, 8.1) (-5.1, 6.7) (3.0, 10.9)

1 and 4

Researchers studying two populations of wolves conducted a two-sample t-test for the difference in means to investigate whether the mean weight of the wolves in one population was different from the mean weight of the wolves in the other population. All conditions for inference were met, and the test produced a test statistic of t=2.771 and a p-value of 0.01. Which of the following is a correct interpretation of the p-value? A Assuming that the mean weights of wolves in the populations are equal, the probability of obtaining a test statistic that is greater than 2.771 or less than −2.771−2.771 is 0.01. B Assuming that the mean weights of wolves in the populations are equal, the probability of obtaining a test statistic that is greater than 2.771 is 0.01. C Assuming that the mean weights of wolves in the populations are different, the probability of obtaining a test statistic that is greater than 2.771 or less than −2.771−2.771 is 0.01. D Assuming that the mean weights of wolves in the populations are different, the probability of obtaining a test statistic that is greater than 2.771 is 0.01. E Assuming that the mean weights of wolves in the populations are different, the probability of obtaining a test statistic that is less than 2.771 is 0.01.

A Assuming that the mean weights of wolves in the populations are equal, the probability of obtaining a test statistic that is greater than 2.771 or less than −2.771−2.771 is 0.01.

A new drug to treat a certain condition is being tested. The null hypothesis of the test is that the drug is not effective. For the researchers, the more consequential error would be for the drug to be effective, but the test does not detect the effect. Which of the following should the researchers do to avoid the more consequential error? A Increase the significance level to increase the probability of Type II error. B Increase the significance level to decrease the probability of Type II error. C Decrease the significance level to increase the probability of Type II error. D Decrease the significance level to decrease the probability of Type II error. E Decrease the significance level to decrease the standard error.

A Increase the significance level to increase the probability of Type II error.

A recent report indicated that families in a certain country typically spend about $175 per week on groceries. To investigate whether families in a certain city typically spend more than $175 per week, an economist selected a random sample of 500 families in the city and found the sample mean to be $176.24. With all conditions for inference met, a hypothesis test resulted in a p-value of 0.0021. At the significance level of α=0.05, which of the following is a correct conclusion? A The pp-value is less than 0.05, and the null hypothesis is rejected. There is convincing statistical evidence that the mean is greater than $175. B The p-value is less than 0.05, and the null hypothesis is not rejected. There is convincing statistical evidence that the mean is greater than $175. C The p-value is less than 0.05, and the null hypothesis is not rejected. There is not convincing statistical evidence that the mean is greater than $175. D The p-value is greater than 0.05, and the null hypothesis is rejected. There is convincing statistical evidence that the mean is greater than $175. E The p-value is greater than 0.05, and the null hypothesis is not rejected. There is not convincing statistical evidence that the mean is greater than $175.

A The p-value is less than 0.05, and the null hypothesis is rejected. There is convincing statistical evidence that the mean is greater than $175.

In a certain region, many of the residents are employed by the oil industry. Economists in the region investigated the difference between the salaries of those who work in oil-field jobs and those who work in non-oil-field jobs. Salaries were recorded for a random sample of 84 workers from the 1,200 oil-field workers and a random sample of 72 workers from the 50,000 non-oil-field workers in the region. A 95 percent confidence interval for μO−μN, where μO is the mean salary of all jobs of oil-field workers and μN is the mean salary of all jobs of non-oil-field workers, will be constructed. Have the conditions for inference with a confidence interval been met? A Yes, all conditions have been met. B No, the data were not collected using a random method. C No, the size of at least one of the samples is greater than 10 percent of the population. D No, the sample sizes are not large enough to assume the distribution of the difference in sample means is normal. E No, the sample sizes are not the same.

A Yes, all conditions have been met.

To estimate the average cost of flowers for summer weddings in a certain region, a journalist selected a random sample of 15 summer weddings that were held in the state. A graph of the sample data showed an approximately symmetric distribution with no outliers. The sample mean and standard deviation were $734 and $102, respectively. The journalist will create a 95 percent confidence interval to estimate the population mean. Have all conditions for inference been met? A Yes, all conditions have been met. B No, the 15 weddings in the sample were not selected at random. C No, the sample size is not large enough to assume the sampling distribution of sample means is approximately normal. D No, because the graphical display is approximately symmetric it cannot be assumed that the sampling distribution of sample means is approximately normal. E No, the sample size of 15 is not less than 10 percent of all weddings in the state.

A Yes, all conditions have been met.

A random sample of 240 adults over the age of 40 found that 144 would use an online dating service. Another random sample of 234 adults age 40 and under showed that 131 would use an online dating service. Assuming all conditions are met, which of the following is the standard error for a 90 percent confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service? A. √144 (1 -( 144)) 131 (1- (131)) --- --- --- --- 240 (240) + 234. (234) -------------- -------------- 240 234

A. √144 (1 -( 144)) 131 (1- (131)) --- --- --- --- 240 (240) + 234. (234) -------------- -------------- 240 234

A recent newspaper article claimed that more people read Magazine A than read Magazine B. To test the claim, a study was conducted by a publishing representative in which newsstand operators were selected at random and asked how many of each magazine were sold that day. The representative will conduct a hypothesis test to test whether the mean number of magazines of type A the operators sell, μA, is greater than the mean number of magazines of type B the operators sell, μB. What are the correct null and alternative hypotheses for the test? A. Ho: μA - μB = 0 HA: μA - μB > 0

A. Ho: μA - μB = 0 HA: μA - μB > 0

Consider a hypothesis test in which the significance level is α=0.05 and the probability of a Type II error is 0.18. What is the power of the test? A 0.95 B 0.82 C 0.18 D 0.13 E 0.05

B 0.82

A sociologist studying the difference in ages between husbands and wives obtained a random sample of 55 married couples. The mean of the husbands' ages was 38.5 years with standard deviation 12.6 years. The mean of the wives' ages was 36.9 years with standard deviation 12.4 years. The sociologist calculated the difference between the ages for each couple. The mean difference was 1.6 years with standard deviation 2.1 years. A matched-pairs hypothesis test will be performed to investigate whether the difference is significant. Which of the following is the standard error for the test statistic for the hypothesis test? A √12.6^2/55 + 12.4^2/55 B 2.1/√55 C 2.1/√55+55 D 12.6-12.4/√55 E 12.6-12.4/√55+55

B 2.1/√55

A sociologist is studying the social media habits of high school students in a school district. The sociologist wants to estimate the average total number of minutes spent on social media per day in the population. A random sample of 50 high school students was selected, and they were asked, "How many minutes per day, on average, do you spend visiting social media sites?" Which of the following is the most appropriate inference procedure for the sociologist to use? A A one-sample z-interval for a population proportion B A one-sample t-interval for a population mean C A matched-pairs t-interval for a mean difference D A two-sample z-interval for a difference between proportions E A two-sample t-interval for a difference between means

B A one-sample t-interval for a population mean

An experiment was conducted to investigate whether there is a difference in mean bag strengths for two different brands of paper sandwich bags. A random sample of 50 bags from each of Brand X and Brand Y was selected. Each bag was held from its rim, and one-ounce weights were dropped into the bag one at a time from the same height until the bag ripped. The number of ounces the bag held before ripping was recorded, and the mean number of ounces for each brand was calculated. Which of the following is the appropriate test for the study? A A matched-pairs t-test for a mean difference B A two-sample t-test for a difference between population means C A two-sample z-test for a difference between population proportions D A two-sample t-test for a difference between sample means E A one-sample z-test for a population proportion

B A two-sample t-test for a difference between population means

The mean number of sick days per employee taken last year by all employees of a large city was 10.6 days. A city administrator is investigating whether the mean number of sick days this year is different from the mean number of sick days last year. The administrator takes a random sample of 40 employees and finds the mean of the sample to be 12.9. A hypothesis test will be conducted as part of the investigation. Which of the following is the correct set of hypotheses? A H0:μ=10.6 Ha:μ>10.6 B H0:μ=10.6 Ha:μ≠10.6 C H0:μ=10.6 Ha:μ<10.6 D H0:μ=12.9 Ha:μ≠12.9 E H0:μ=12.9 Ha:μ<12.9

B H0:μ=10.6 Ha:μ≠10.6

Hannah claims that people who live in southern states spend 9 hours more per week outside than do people in northern states. She selects a random sample from each group. The mean number of hours per week that people in southern states spent outside is 18.6, and the mean number of hours per week that people in northern states spent outside is 14.4. A 99 percent confidence interval to estimate the difference in population means (southern minus northern) is (0.4,8.0). Which of the following statements about Hannah's claim is supported by the interval? A Hannah is likely to be incorrect because the difference in the sample means was 18.6−14.4=4.218.6−14.4=4.2 hours. B Hannah is likely to be incorrect because 9 is not contained in the interval. C The probability that Hannah is correct is 0.99 because 9 is not contained in the interval. D The probability that Hannah is correct is 0.01 because 9 is not contained in the interval. E Hannah is likely to be correct because the difference in the sample means (18.6−14.4=4.2)(18.6−14.4=4.2) is contained in the interval.

B Hannah is likely to be incorrect because 9 is not contained in the interval.

A local convenience store in a large city closes each day at 10 P.M. The owner of the store is investigating whether mean sales will increase by at least $10 per day if the store remains open until 11 P.M. The owner asked the 41 members of a local civic group to estimate the amount of money they might spend during the extra hour. The sample mean was $11.50. The owner will conduct a one-sample t-test for a population mean. Have the conditions for inference been met? A Yes, all conditions have been met. B No, the sample was not chosen using a random method. C No, the sample size is greater than 10 percent of the population. D No, the sample size is not large enough to assume normality of the sampling distribution. E No, the distribution of the sample is not normal.

B No, the sample was not chosen using a random method.

A two-sample t-test for a difference in means was conducted to investigate whether there is a statistically significant difference in the average amount of fat found in low-fat yogurt and the average amount of fat found in nonfat yogurt. With all conditions for inference met, the test produced a test statistic of t=2.201 and a p-value of 0.027. Based on the p-value and a significance level of α=0.05, which of the following is the correct conclusion? A Reject the null hypothesis because p<αp<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is not statistically significant. B Reject the null hypothesis because p<αp<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is statistically significant. C Fail to reject the null hypothesis because p<αp<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is not statistically significant. D Fail to reject the null hypothesis because p>αp>α. The difference in the average amount of fat found in low-fat and nonfat yogurt is statistically significant. E Fail to reject the null hypothesis because p>αp>α. The difference in the average amount of fat found in low-fat and nonfat yogurt is not statistically significant.

B Reject the null hypothesis because p<αp<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is statistically significant.

A certain ambulance service wants its average time to transport a patient to the hospital to be 10 minutes. A random sample of 12 transports yielded a 95 percent confidence interval of 11.8±1.6 minutes. Is the claim that the ambulance service takes an average of 10 minutes to transport a patient to the hospital plausible based on the interval? A The claim is not plausible because 10 falls within the interval. B The claim is not plausible because 10 falls outside of the interval. C The claim is plausible because 10 falls within the interval. D The claim is plausible because 10 falls outside of the interval. E The claim is plausible because 10 falls within 0.95 units of the interval.

B The claim is not plausible because 10 falls outside of the interval.

Researchers studying the sticky droplets found on spider webs will measure the widths of a random sample of droplets. From the sample, the researchers will construct a 95 percent confidence interval to estimate the mean width of all such droplets. Which of the following statements about a 95 percent confidence interval for the mean width is correct? A The interval will be narrower if the researchers increase the level of confidence to 99 percent. B The interval will be narrower if the researchers increase the sample size of droplets. C The interval will be wider if the researchers decrease the level of confidence to 90 percent. D The interval will be wider if the researchers increase the sample size of droplets. E The width of the interval will not be affected if the researchers increase or decrease the number of droplets in the sample.

B The interval will be narrower if the researchers increase the sample size of droplets.

Machines at a factory produce circular washers with a specified diameter. The quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. The null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. The alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent. Which of the following describes a Type I error that could result from the test? A The test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. B The test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. C The test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. D The test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. E A Type II error is not possible for this hypothesis test.

B The test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%.

A consumer group selected 100 different airplanes at random from each of two large airlines. The mean seat width for the 100 airplanes was calculated for each airline, and the difference in the sample mean widths was calculated. The group used the sample results to construct a 95 percent confidence interval for the difference in population mean widths of seats between the two airlines. Suppose the consumer group used a sample size of 50 instead of 100 for each airline. When all other things remain the same, what effect would the decrease in sample size have on the interval? A The width of the confidence interval would decrease. B The width of the confidence interval would increase. C The width of the confidence interval would remain the same. D The level of confidence would increase. E The level of confidence would decrease.

B The width of the confidence interval would increase.

A two-sample t-test for a difference in means was conducted to investigate whether the average wait time at a fast food restaurant in Town A was longer than the average wait time at a fast food restaurant in Town B. With all conditions for inference met, the test produced a test statistic of t=2.42 and a p-value of 0.011. Based on the p-value and a significance level of α=0.02, which of the following is a correct conclusion? A There is convincing statistical evidence that the average wait times at the two restaurants are the same. B There is convincing statistical evidence that the average wait time at the restaurant in Town A is longer than the average wait time at the restaurant in Town B. C There is convincing statistical evidence that the average wait times at the two restaurants are different. D There is not convincing statistical evidence that the average wait times at the two restaurants are the same. E There is not convincing statistical evidence that the average wait time at the restaurant in Town A is longer than the average wait time at the restaurant in Town B.

B There is convincing statistical evidence that the average wait time at the restaurant in Town A is longer than the average wait time at the restaurant in Town B.

Two ride-sharing companies, A and B, provide service for a certain city. A random sample of 52 trips made by Company A and a random sample of 52 trips made by Company B were selected, and the number of miles traveled for each trip was recorded. The difference between the sample means for the two companies (A−B) was used to construct the 95 percent confidence interval (1.86,2.15). Which of the following is a correct interpretation of the interval? A We are 95 percent confident that the difference in sample means for miles traveled by the two companies is between 1.86 miles and 2.15 miles. B We are 95 percent confident that the difference in population means for miles traveled by the two companies is between 1.86 miles and 2.15 miles. C The probability is 0.95 that the difference in sample means for miles traveled by the two companies is between 1.86 miles and 2.15 miles. D The probability is 0.95 that the difference in population means for miles traveled by the two companies is between 1.86 miles and 2.15 miles. E About 95 percent of the differences in miles traveled by the two companies are between 1.86 miles and 2.15 miles.

B We are 95 percent confident that the difference in population means for miles traveled by the two companies is between 1.86 miles and 2.15 miles.

A linguist at a large university was studying the word length of papers submitted by students enrolled in humanities programs. From a random sample of 25 papers, the linguist counted the number of words used in each paper. The 95 percent confidence interval was calculated to be (20,995, 22,905). Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval? A We are 95 percent confident that the mean word length for the papers submitted by students in the sample is between 20,995 words and 22,905 words. B We are 95 percent confident that the mean word length for all papers submitted by students in humanities programs is between 20,995 words and 22,905 words. C The probability is 0.95 that the mean word length for the papers submitted by students in the sample is between 20,995 words and 22,905 words. D The probability is 0.95 that the mean word length for all papers submitted by students in humanities programs is between 20,995 words and 22,905 words. E For all students in humanities programs who submit papers, 95 percent of the papers are between 20,995 words and 22,905 words.

B We are 95 percent confident that the mean word length for all papers submitted by students in humanities programs is between 20,995 words and 22,905 words.

A two-sample t-test will be conducted to investigate whether the mean number of tickets sold for children each day is less at movie theater J than at movie theater K. From a random sample of 50 days at theater J, the average was 75 children tickets with standard deviation 12. From a random sample of 60 days at theater K, the average was 85 children tickets with standard deviation 14. Under the assumption that there is no difference in the population means (J minus K), which of the following is the appropriate test statistic for the test? B. t = 75-85/√12^2/50 + 14^2/60

B. t = 75-85/√12^2/50 + 14^2/60

To study the effectiveness of a certain adult reading program, researchers will select a random sample of adults who are eligible for the program. The selected adults will be given a pretest before beginning the program and a posttest after completing the program. The difference in the number of correct answers on the pretest and the number of correct answers on the posttest will be recorded for each adult in the sample. Which of the following is the most appropriate inference procedure for the researchers to use to analyze the results? A A one-sample z-interval for a population proportion B A one-sample t-interval for a sample mean difference C A matched-pairs t-interval for a population mean difference D A matched-pairs t-interval for a sample mean difference E A two-sample t-interval for a difference between means

C A matched-pairs t-interval for a population mean difference

A researcher is investigating whether a new fertilizer affects the yield of tomato plants. As part of an experiment, 20 plants will be randomly assigned the new fertilizer and 20 will be assigned the current fertilizer. The mean number of tomatoes produced per plant will be recorded for each fertilizer, and the difference in the sample means will be calculated. Which of the following is the appropriate inference procedure for analyzing the results of the experiment? A A matched-pairs t-interval for a mean difference B A two-sample t-interval for a difference between sample means C A two-sample t-interval for a difference between population means D A one-sample t-interval for a sample mean E A one-sample t-interval for a population mean

C A two-sample t-interval for a difference between population means

A random sample of monarch butterflies and a random sample of swallowtail butterflies were selected, and the difference in the average flying speed for each sample was calculated. A two-sample t-test for the difference in means was conducted to investigate whether the speed at which monarchs fly, on average, is faster than the speed at which swallowtails fly. All conditions for inference were met, and the p-value was given as 0.072. Which of the following is a correct interpretation of the p-value? A The probability that monarchs fly faster than swallowtails is 0.072. B The probability that monarchs and swallowtails fly at the same speed is 0.072. C Assuming that monarchs and swallowtails fly at the same speed on average, the probability of observing a difference equal to or greater than the sample difference is 0.072. D Assuming that monarchs fly faster than swallowtails on average, the probability of observing a difference equal to or greater than the sample difference is 0.072. E Assuming that monarchs fly faster than swallowtails on average, the probability of the monarchs and swallowtails flying at the same speed is 0.072.

C Assuming that monarchs and swallowtails fly at the same speed on average, the probability of observing a difference equal to or greater than the sample difference is 0.072.

A company director investigated whether there is a difference in the mean number of overtime hours worked each week by employees assigned to two different managers. Each manager, A and B, manages 100 employees. Random samples of 35 employees from manager A and 40 employees from manager B were selected. The number of overtime hours worked was recorded for the 75 employees each week. Have the conditions been met for inference with a confidence interval for the difference in the population means? A Yes, all conditions have been met. B No, because the data were not collected using a random method. C No, because the size of at least one of the samples is greater than 10 percent of the population. D No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is normal. E No, because the sample sizes are not the same.

C No, because the size of at least one of the samples is greater than 10 percent of the population.

In certain regions of the country, elk can cause damage to agricultural crops by walking through the fields. One strategy designed to limit elk from crossing a field is to surround the field with a fence. Some elk, however, will still be able to bypass the fence. For a period of one month, the number of elk found crossing a sample of fields with a fence was recorded and used to construct the 95 percent confidence interval (2.9,4.4) for the mean number of elk. Assume that the conditions for inference were checked and verified. The interval (2.9,4.4) provides convincing statistical evidence for which of the following claims? A The mean number of elk to cross a field protected by a fence is 4 per month. B The mean number of elk to cross a field protected by a fence is 2 per month. C The mean number of elk to cross all fields protected by a fence is greater than 2 per month. D The mean number of elk to cross all fields protected by a fence is less than 2 per month. E The mean number of elk to cross all fields protected by a fence is equal to 3.65 per month.

C The mean number of elk to cross all fields protected by a fence is greater than 2 per month.

A recent increase in sales of microchips has forced a computer company to buy a new processing machine to help keep up with demand. The builders of the new machine claim that it produces fewer defective microchips than the older machine. From a random sample of 90 microchips produced on the old machine, 5 were found to be defective. From a random sample of 83 microchips produced on the new machine, 3 were found to be defective. The quality control manager wants to construct a confidence interval to estimate the difference between the proportion of defective microchips from the older machine and the proportion of defective microchips from the new machine. Why is it not appropriate to calculate a two-sample z-interval for a difference in proportions? A The microchips were not randomly assigned to a machine. B There is no guarantee that microchips are approximately normally distributed. C The normality of the sampling distribution of the difference in sample proportions cannot be established. D Both sample proportions are less than 0.10. E The sample sizes are not the same.

C The normality of the sampling distribution of the difference in sample proportions cannot be established.

At a manufacturing company, the percent of defective items produced on the assembly line is 2%. The company is testing a new assembly line designed to reduce the percent of defective parts. The null and alternative hypotheses of the test are described as follows. H0:The percent of defective parts is at least 2%.Ha:The percent of defective parts is less than 2%. Which of the following describes a Type II error that could result from the test? A The test does not provide convincing evidence that the percent is less than 2%, but the actual percent is 3%. B The test does not provide convincing evidence that the percent is less than 2%, but the actual percent is 2%. C The test does not provide convincing evidence that the percent is less than 2%, but the actual percent is 1%. D The test provides convincing evidence that the percent is less than 2%, but the actual percent is 2%. E The test provides convincing evidence that the percent is less than 2%, but the actual percent is 1%.

C The test does not provide convincing evidence that the percent is less than 2%, but the actual percent is 1%.

A group of AP Chemistry students debated which fast-food chain had better quality bags, Fast Food Chain W or Fast Food Chain M . They decided to investigate by selecting a random sample of 25 bags from each fast food restaurant, slowly adding water until each bag began to leak, and recording the volume of water they were able to pour into each bag. They then calculated the mean volume and standard deviation, in ounces, for the two types of bags. Which of the following are the correct null and alternative hypotheses to test whether the mean volume of water the bags from Fast Food Chain W can hold without leaking, μW, is different from that for the bags from Fast Food Chain M, μM ? C. Ho: μW - μM = 0 HA: μW - μM ≠ 0

C. Ho: μW - μM = 0 HA: μW - μM ≠ 0

A random sample of 100 people from Country S had 15 people with blue eyes. A separate random sample of 100 people from Country B had 25 people with blue eyes. Assuming all conditions are met, which of the following is a 95 percent confidence interval to estimate the difference in population proportions of people with blue eyes (Country S minus Country B) ? A (−0.01,0.21) B (−0.15,−0.05) C (−0.19,−0.01) D (−0.21,0.01) E (−0.24,0.04)

D (−0.21,0.01)

A recent study of 1,215 randomly selected middle school students revealed that the average number of minutes they spent completing homework during the school week was 180 minutes with a standard deviation of 45 minutes. Which of the following is the standard error, in minutes, of the sampling distribution of the mean number of minutes spent on homework per week for all middle school students? A √(45(55)/1215 B 45/1215 C √45/1215 D 45/√1215 E 1.96(45/√1215)

D 45/√1215

A travel company is investigating whether the average cost of a hotel stay in a certain city has increased over the past year. The company recorded the cost of a one-night stay for a Friday night in January of the current year and in the previous year for 31 hotels selected at random. The difference in cost (current year minus previous year) was calculated for each hotel. Which of the following is the appropriate test for the company's investigation? A A one-sample z-test for a population mean B A one-sample t-test for a sample mean C A one-sample z-test for a population proportion D A matched-pairs t-test for a mean difference E A two-sample t-test for a difference between means

D A matched-pairs t-test for a mean difference

A marketing executive is investigating whether this year's advertising campaign has resulted in greater mean sales compared with last year's mean sales. The executive collects a random sample of 100 customer orders from a large population of orders and calculates the sample mean and sample standard deviation. Which of the following is the appropriate test for the executive's investigation? A A one-sample z-test for a population mean B A one-sample t-test for a population mean C A one-sample z-test for a population proportion D A two-sample t-test for a difference between means E A matched-pairs t-test for a mean difference

D A two-sample t-test for a difference between means

A study will be conducted to investigate whether there is a difference in the mean weights between two populations of raccoons. Random samples of raccoons will be selected from each population, and the mean sample weight will be calculated for each sample. Which of the following is the appropriate test for the study? A A one-sample z-test for a population proportion B A one-sample t-test for a population mean C A two-sample t-test for a difference between sample means D A two-sample t-test for a difference between population means E A two-sample z-test for a difference between population proportions

D A two-sample t-test for a difference between population means

Researchers are testing a new diagnostic tool designed to identify a certain condition. The null hypothesis of the significance test is that the diagnostic tool is not effective in detecting the condition. For the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective. Which of the following should the researchers do to avoid the more consequential error? A Increase the significance level to increase the probability of Type II error. B Increase the significance level to decrease the probability of Type II error. C Decrease the significance level to increase the probability of Type II error. D Decrease the significance level to decrease the probability of Type II error. E Decrease the significance level to decrease the standard error.

D Decrease the significance level to decrease the probability of Type II error.

Donald believes that western commuters drive an average of 10 miles more per day than eastern commuters do. He selects random samples from each group. The western mean is 23.5 miles, and the eastern mean is 19.4 miles. A 95 percent confidence interval to estimate the difference in population means, in miles, is (2.5,5.7). Which of the following statements is supported by the interval? A The probability that Donald is correct is 0.05 because 10 is not contained in the interval. B The probability that Donald is correct is 0.95 because 10 is not contained in the interval. C Donald is likely to be correct because the difference in the sample means (23.5−19.4=4.1)(23.5−19.4=4.1) is contained in the interval. D Donald is likely to be incorrect because 10 is not contained in the interval. E Donald is likely to be incorrect because the difference in the sample means was 23.5−19.4=4.123.5−19.4=4.1 miles.

D Donald is likely to be incorrect because 10 is not contained in the interval.

A report on a certain fast food restaurant states that μ, the mean order total, is $9. The manager of the restaurant believes the mean is higher. A random sample of orders will be selected. The sample mean x¯ will be calculated and used in a hypothesis test to investigate the belief. Which of the following is the correct set of hypotheses? A H0:x =$9 Ha:x ≠$9 B H0:x =$9 Ha: x>$9 C H0:μ=$9 Ha:μ≠$9 D H0:μ=$9 Ha:μ>$9 E H0:μ=$9 Ha:μ<$9

D H0:μ=$9 Ha:μ>$9

At a high school with over 500 students, a counselor wants to estimate the mean number of hours per week that students at the school spend in community service activities. The counselor will survey 20 students in the Environmental Club at the school. The mean number of hours for the 20 students will be used to estimate the population mean. Which of the following conditions for inference have not been met? The data are collected using a random sampling method. The sample size is large enough to assume normality of the distribution of sample means. The sample size is less than 10 percent of the population size. A I only B II only C III only D I and II only E II, IIII, and III

D I and II only

Which of the following indicates that the use of a two-sample z-interval for a difference in population proportions is appropriate? Two populations of interest exist. The variable of interest is categorical. The intent is to estimate a difference in sample proportions. A I only B II only C III only D I and II only E I, II, and III

D I and II only

Two community service groups, J and K, each have less than 100 members. Members of both groups volunteer each month to participate in a community-wide recycling day. A study was conducted to investigate whether the mean number of days per year of participation was different for the two groups. A random sample of 45 members of group J and a random sample of 32 members of group K were selected. The number of recycling days each selected member participated in for the past 12 months was recorded, and the means for both groups were calculated. A two-sample t-test for a difference in means will be conducted. Which of the following conditions for inference have been met? The data were collected using a random method. Each sample size is less than 10 percent of the population size. Each sample size is large enough to assume normality of the sampling distribution of the difference in sample means. A I only B II only C III only D I and III only E I, II, and III

D I and III only

An agency that hires out clerical workers claims its workers can type, on average, at least 60 words per minute (wpm). To test the claim, a random sample of 50 workers from the agency were given a typing test, and the average typing speed was 58.8 wpm. A one-sample t-test was conducted to investigate whether there is evidence that the mean typing speed of workers from the agency is less than 60 wpm. The resulting p-value was 0.267. Which of the following is a correct interpretation of the p-value? A The probability is 0.267 that the mean typing speed is 60 wpm or more for workers from the agency. B The probability is 0.267 that the mean typing speed is 60 wpm or less for workers from the agency. C The probability is 0.267 that the mean typing speed is 58.8 wpm or less for workers from the agency. D If the mean typing speed of workers from the agency is 60 wpm, the probability of selecting a sample of 50 workers with mean 58.8 wpm or less is 0.267. E If the mean typing speed of workers from the agency is less than 60 wpm, the probability of selecting a sample of 50 workers with mean 58.8 wpm or less is 0.267.

D If the mean typing speed of workers from the agency is 60 wpm, the probability of selecting a sample of 50 workers with mean 58.8 wpmor less is 0.267.

A civil engineer tested concrete samples to investigate the difference in strength, in newtons per square millimeter (N/mm2), between concrete hardened for 21 days and concrete hardened for 28 days. The engineer measured the strength from each sample, calculated the difference in the mean strength between the samples, and then constructed the 95 percent confidence interval, (2.9,3.1), for the difference in mean strengths. Assuming all conditions for inference were met, which of the following is a correct interpretation of the 95 percent confidence level? A In repeated samples of the same size, approximately 95 percent of the samples will yield the interval 2.9 N/mm2N/mm2 to 3.1 N/mm2N/mm2. B In repeated samples of the same size, approximately 95 percent of the sample means will fall between 2.9 N/mm2N/mm2 and 3.1 N/mm2N/mm2. C In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will extend from 2.9 N/mm2N/mm2 to 3.1 N/mm2N/mm2. D In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the population difference in means. E In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the sample difference in means.

D In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the population difference in means.

A study was conducted to investigate whether the mean numbers of snack bars sold at two airport convenience stores, C and D, were different. For ten randomly selected days, the number of snack bars sold at each store was recorded, and the sample mean number of snack bars for each store was calculated. A two-sample t-test for a difference in means will be conducted. Have all conditions for inference been met? A Yes, all conditions have been met. B No, the data were not collected using a random method. C No, the sample sizes are greater than 10 percent of the population. D No, the sample sizes are not large enough to assume normality of the sampling distribution. E No, the distribution of the population is known to be skewed.

D No, the sample sizes are not large enough to assume normality of the sampling distribution.

In a certain city, the population mean commute time to work was reported as 30 minutes. The director of human resources for a certain company in the city claimed the mean commute time for the company's employees was greater than 30 minutes. The director surveyed 35 randomly selected employees and found that their mean commute time was 31.4 minutes. With all conditions for inference met, a hypothesis test conducted at the significance level α=0.05 resulted in a p-value of 0.381. Which of the following is an appropriate conclusion? A The director has convincing statistical evidence to conclude that the population mean commute time is greater than 30 minutes. B The director has convincing statistical evidence to conclude that the population mean commute time is less than 30 minutes. C The director has convincing statistical evidence to conclude that the population mean commute time is 31.4 minutes. D The director does not have convincing statistical evidence to conclude that the population mean commute time is greater than 30 minutes. E The director does not have convincing statistical evidence to conclude that the population mean commute time is less than 30 minutes.

D The director does not have convincing statistical evidence to conclude that the population mean commute time is greater than 30 minutes.

Which of the following is defined by the significance level of a hypothesis test? A The standard error B The power of the test C The probability of Type II error D The probability of Type I error E The p-value

D The probability of Type I error

If all other factors are held constant, which of the following results in a decrease in the probability of a Type II error? A The true parameter is closer to the value of the null hypothesis. B The sample size is decreased. C The significance level is decreased. D The standard error is decreased. E The probability of a Type IIII error cannot be decreased, only increased.

D The standard error is decreased.

Two 95 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and J. One confidence interval, I400, will be constructed using samples of size 400 from each of R and J, and the other confidence interval, I100, will be constructed using samples of size 100 from each of R and J. When all other things remain the same, which of the following describes the relationship between the two confidence intervals? A The width of I400will be 4 times the width of I100 B The width of I400 will be 2 times the width of I100. C The width of I400 will be equal to the width of I100. D The width of I400 will be 1/2 times the width of I100. E The width of I400 will be 1/4 times the width of I100.

D The width of I400 will be 1/2 times the width of I100.

A company that manufactures laptop batteries claims the mean battery life is 16 hours. Assuming the distribution of battery life is approximately normal, a consumer group will conduct a hypothesis test to investigate whether the battery life is less than 16 hours. The group selected a random sample of 14 of the batteries and found an average life of 15.6 hours with a standard deviation of 0.8 hour. Which of the following is the correct test statistic for the hypothesis test? A t= (15.6−16)/0.8 B t= (16−15.6)/0.8 C t= (15.6-16)/(0.8)/√13 D t= (15.6−16)(0.8)/√14 E t= (16-15.6)/(0.8)/√14

D t= (15.6−16)(0.8)/√14

A researcher is investigating whether a difference exists in the mean weight of green-striped watermelons grown on two different farms: one that uses organic methods and one that uses nonorganic methods. The mean and standard deviation of the weights in a random sample of 43 watermelons from the organic farm were 18 pounds and 2 pounds, respectively. The mean and standard deviation of the weights in a random sample of 40 watermelons from the nonorganic farm were 20 pounds and 1.7 pounds, respectively. Which of the following represents the standard error of the difference in the mean weights of watermelons from the two farms? A 2+1.7 B √2/43 + 1.7/40 C 2/√43 + 1.7/√40 D √2^2/43 + 1.7^2/40 E √2^2 + 1.7^2/43+40

D √2^2/43 + 1.7^2/40

A two-sample t-test for a difference in means will be conducted to investigate whether the average amount of money spent per customer at Department Store M is different from that at Department Store V. From a random sample of 35 customers at Store M, the average amount spent was $300 with standard deviation $40. From a random sample of 40 customers at Store V, the average amount spent was $290 with standard deviation $35. Assuming a null hypothesis of no difference in population means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (Department Store M minus Department Store V) ? D. t= 300-290/√40^2/35 + 35^2/40

D. t= 300-290/√40^2/35 + 35^2/40

The mean and standard deviation of a random sample of 7 baby orca whales were calculated as 430 pounds and 26.9 pounds, respectively. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the mean weight of all baby orca whales? A 26.9±1.895(430/√7) B 26.9±1.943(430/√7) C 430±1.440(26.9/√7) D 430±1.895(26.9/√7) E 430±1.943(26.97√7)

E 430±1.943(26.97√7)

An occupational safety officer for a large company is conducting a study to investigate back problems in office workers who use a computer for most of the workday. The study will investigate the difference in back problems for workers who stand and workers who sit. A group of 68 volunteers have agreed to participate in the nine-month study. Half the group is randomly assigned to work while standing, and the other half is assigned to work while sitting. At the end of the study, the mean number of back problems between the two groups will be calculated. The officer will use the results to estimate the difference in the mean number of back problems between those who work while standing and those who work while sitting. Which of the following is an appropriate inference procedure for the study? A A one-sample t-interval for a population mean B A one-sample t-interval for a sample mean C A matched pairs t-interval for a mean difference D A two-sample t-interval for a difference between sample means E A two-sample t-interval for a difference between population means

E A two-sample t-interval for a difference between population means

At a research facility that designs rocket engines, researchers know that some engines fail to ignite as a result of fuel system error. From a random sample of 40 engines of one design, 14 failed to ignite as a result of fuel system error. From a random sample of 30 engines of a second design, 9 failed to ignite as a result of fuel system error. The researchers want to estimate the difference in the proportion of engine failures for the two designs. Which of the following is the most appropriate method to create the estimate? A A one-sample z-interval for a sample proportion B A one-sample z-interval for a population proportion C A two-sample z-interval for a population proportion D A two-sample z-interval for a difference in sample proportions E A two-sample z-interval for a difference in population proportions

E A two-sample z-interval for a difference in population proportions

A consumer group wants to know if an automobile insurance company with thousands of customers has an average insurance payout for all their customers that is greater than $500 per insurance claim. They know that most customers have zero payouts and a few have substantial payouts. The consumer group collects a random sample of 18 customers and computes a mean payout per claim of $579.80 with a standard deviation of $751.30. Is it appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers? A Yes, it is appropriate because the population standard deviation is unknown. B Yes, it is appropriate because the sample size is large enough, so the condition that the sampling distribution of the sample mean be approximately normal is satisfied. C No, it is not appropriate because the sample is more than 10 percent of the population, so a condition for independence is not satisfied. D No, it is not appropriate because the standard deviation is greater than the mean payout, so the condition that the sampling distribution of the sample mean be approximately normal is not satisfied. E No, it is not appropriate because the distribution of the population is skewed and the sample size is not large enough to satisfy the condition that the sampling distribution of the sample mean be approximately normal.

E No, it is not appropriate because the distribution of the population is skewed and the sample size is not large enough to satisfy the condition that the sampling distribution of the sample mean be approximately normal.

What happens to a t-distribution as the degrees of freedom increase? A The center increases, and the area in the tails increases. B The center increases, and the area in the tails decreases. C The center increases, and the area in the tails remains constant. D The center remains constant, and the area in the tails increases. E The center remains constant, and the area in the tails decreases.

E The center remains constant, and the area in the tails decreases.

A researcher studying the sleep habits of teens will select a random sample of n teens from the population to survey. The researcher will construct a t-interval to estimate the mean number of hours of sleep that teens in the population get each night. Which of the following is true about the t-distribution as the value of n decreases from 40 to 20 ? A The center decreases, and the area in the tails of the distribution increases. B The center increases, and the area in the tails of the distribution decreases. C The center remains constant, and the area in the tails of the distribution remains constant. D The center remains constant, and the area in the tails of the distribution decreases. E The center remains constant, and the area in the tails of the distribution increases.

E The center remains constant, and the area in the tails of the distribution increases.

Milk has a pH of 6.7, which is slightly acidic. Cheese makers add a culture to milk to lower the pH, making it more acidic and turning it into cheese. A manufacturer is experimenting with a new culture that claims to produce a pH of 5.2, which is perfect for cheddar cheese. A set of 50 test batches resulted in an average pH of 5.11. A one-sample t-test was conducted to investigate whether there is evidence that the mean pH is different from 5.2. The test resulted in a p-value of 0.018. Which of the following is a correct interpretation of the p-value? A The probability that the true pHpH is equal to 5.2 is 0.018. B The probability that the true pHpH is different from 5.2 is 0.018. C The probability of observing a sample mean of 5.11 or less is 0.018 if the true mean is 5.2. D The probability of observing a sample mean of 5.11 or more is 0.018 if the true mean is 5.2. E The probability of observing a sample mean of 5.11 or less, or of 5.29 or more, is 0.018 if the true mean is 5.2.

E The probability of observing a sample mean of 5.11 or less, or of 5.29 or more, is 0.018 if the true mean is 5.2.

Researchers collected two different samples, X and Y, of temperatures, in degrees Celsius, of the habitat for Florida scrub lizards. The confidence interval 36±1.66 was constructed from sample X, and the confidence interval 36±1.08 was constructed from sample Y. Assume both samples had the same standard deviation. Which of the following statements could explain why the width of the confidence interval constructed from X is greater than the width of the confidence interval constructed from Y? A The sample size of X is greater than the sample size of Y, and the confidence level is the same for both intervals. B The sample size of X is greater than the sample size of Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y. C The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y. D The sample size is the same for X and Y, and the confidence level is the same for both intervals. E The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y.

E The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y.

A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in northern Colorado. To estimate the difference between the proportions of deer with chronic wasting disease in two different regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region. The biologist checked for the following. (200)(0.06)≥10(200)(0.94)≥10(197)(0.086)≥10(197)(0.914)≥10 Which of the following conditions for inference was the biologist checking? A The population of deer within each region is approximately normal. B It is reasonable to generalize from the samples to the populations. C The samples are independent of each other. D The observations within each sample are close to independent. E The sampling distribution of the difference in sample proportions is approximately normal.

E The sampling distribution of the difference in sample proportions is approximately normal.

Sociologists studying the behavior of high school freshmen in a certain state collected data from a random sample of freshmen in the population. They constructed the 90 percent confidence interval 6.46±0.41 for the mean number of hours per week spent by freshmen in extracurricular activities. Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval? A For all freshmen in the state, 90 percent of the freshmen spend between 6.05 hours and 6.87 hours per week in extracurricular activities. B The probability is 0.90 that the mean number of hours spent in extracurricular activities for freshmen in the sample is between 6.05 hours and 6.87 hours per week. C The probability is 0.90 that the mean number of hours spent in extracurricular activities for freshmen in the state is between 6.05 hours and 6.87 hours per week. D We are 90 percent confident that the mean number of hours spent in extracurricular activities for freshmen in the sample is between 6.05 hours and 6.87 hours per week. E We are 90 percent confident that the mean number of hours spent in extracurricular activities for freshmen in the state is between 6.05 hours and 6.87 hours per week.

E We are 90 percent confident that the mean number of hours spent in extracurricular activities for freshmen in the state is between 6.05 hours and 6.87 hours per week.

The null hypothesis for a particular experiment is that the mean test score is 20. If the 99% confidence interval is (18, 24), can you reject the null hypothesis at the .01 level? Yes No

No

If a 95% confidence interval contains 0, so will the 99% confidence interval. True False

True