STATS FINAL

In 2010, a medical research group reported the results of an experiment to evaluate the effectiveness of acupuncture to treat a chronic intestinal condition. A group of volunteers with the chronic intestinal condition agreed to participate in the experiment and be randomly assigned to either a true acupuncture treatment or a placebo treatment. The placebo treatment mimicked the application of acupuncture, but no needle penetrated the skin. Random assignment resulted in 78 subjects receiving acupuncture and 75 subjects receiving the placebo treatment. After receiving 6 treatments over the course of 3 weeks, patients were asked to report whether they had experienced a reduction in the chronic intestinal condition. The table summarizes the data from the study, with expected cell counts in parentheses. YesNoTotalAcupuncture41 (37.2)37 (40.8)78Placebo treatment32 (35.8)43 (39.2)75Total7380153 Which of the following is true about the chi-square test for homogeneity? A The number of subjects randomly assigned to each treatment is not the same; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups. B Volunteers do not constitute a random sample from the population of all patients with the chronic intestinal condition; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups. C Volunteers with the chronic intestinal condition were randomly assigned to each treatment, so the independence condition has been met. D Not all of the observed cell counts are large enough to satisfy the conditions for applying the chi-square test of homogeneity. E Not all of the expected cell counts are large enough to satisfy the conditions for applying the chi-square test for homogeneity.

Volunteers with the chronic intestinal condition were randomly assigned to each treatment, so the independence condition has been met.

A certain statistic dˆd^ is being used to estimate a population parameter DD. The expected value of dˆd^ is not equal to DD. What property does dˆd^ exhibit? A The sampling distribution of dˆd^ is normal. B The sampling distribution of dˆd^ is binomial. C The sampling distribution of dˆd^ is uniform. D dˆd^ is unbiased. E dˆd^ is biased.

e-dˆd^ is biased.

According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor's degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable BB represent the number in the sample who have a bachelor's degree. What is the probability that BB will equal 40 ? A (5040)(0.31)40(0.69)10(5040)(0.31)40(0.69)10 B (5040)(0.69)40(0.31)10(5040)(0.69)40(0.31)10 C (4010)(0.31)40(0.69)10(4010)(0.31)40(0.69)10 D (4010)(0.69)40(0.31)10(4010)(0.69)40(0.31)10 E 40(0.31)50

A (5040)(0.31)40(0.69)10

A scientist is investigating whether percent concentration can be used to predict density in apple juice. A scientist selected a random sample of 12 apple juice varieties and recorded the density, in pounds per cubic inch, and the percent concentration of each apple juice variety. The scientist wants to estimate the mean change in the density, in pounds per cubic inch, for each increase of 1 percent concentration of apple juice. Assuming the conditions for inference have been met, which of the following inference procedures is most appropriate for this investigation? A A linear regression tt-interval for slope B A matched-pairs tt-interval for a mean difference C A two-sample tt-interval for a difference between means D A one-sample tt-test for means E A two-sample zz-interval for a difference between proportions

A A linear regression tt-interval for slope

In a certain region, 94 percent of the people have a certain characteristic in their blood. Suppose a group of 45 people from the region are selected at random. Let the random variable BB represent the number of people in the sample without the characteristic. Random variable BB follows a binomial distribution with a mean of 2.7 people. Which of the following is the best interpretation of the mean? A For all groups of 45 people, the average number of people without the characteristic is 2.7. B Every group of 45 people will have 2.7 people with the characteristic. C Every group of 45 people will have 2.7 people without the characteristic. D On average, 2.7 people are selected until finding someone with the characteristic. E On average, 2.7 people are selected until finding someone without the characteristic.

A For all groups of 45 people, the average number of people without the characteristic is 2.7.

In two common species of flowers, A and B, the proportions of flowers that are blue are pa and pb , respectively. Suppose that independent random samples of 50 species-A flowers and 100 species-B flowers are selected. Let pˆa be the sample proportion of blue species-A flowers and pˆb be the sample proportion of blue species-B flowers. What is the mean of the sampling distribution of pˆa−pˆb ? A pa−pb B pa50−pb100 C pˆa−pˆb D pa(1−pa)50+pb(1−pb)100 E pa(1−pa)50+pb(1−pb)100−−−−−−−−−−−−−−√

A pa−pbpa−pb

For a certain brand of canned corn, the company claims that the mean weight of the contents of the cans is 15.25 ounces. A random sample of 36 cans were selected. The sample was found to have mean 15.18 ounces and standard deviation 0.12 ounce. A hypothesis test will be conducted to investigate whether there is evidence to support the belief that the mean is less than 15.25 ounces. Which of the following is the correct test statistic for the hypothesis test? A t=15.18−15.250.126t=15.18−15.250.126 B t=15.18−15.250.1236t=15.18−15.250.1236 C t=15.25−15.180.126t=15.25−15.180.126 D t=15.25−15.180.1236t=15.25−15.180.1236 E t=15.25−15.180.12

A t=15.18−15.250.126t=15.18−15.250.126

A fair six-sided die, with sides numbered 1 through 6, will be rolled a total of 15 times. Let x¯1x¯1 represent the average of the first ten rolls, and let x¯2x¯2 represent the average of the remaining five rolls. What is the mean μ(x¯1−x¯2)μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2 ? A 3.510−3.55=−0.353.510−3.55=−0.35 B 3.5−3.5=03.5−3.5=0 C 10−5=510−5=5 D 10(3.5)−5(3.5)=17.510(3.5)−5(3.5)=17.5 E 6(10−5)=30

B 3.5−3.5=0

The number of shots taken and points scored by 8 players in a basketball game are shown in the table. Number of shots taken147810111114Number of points scored048914121522 A basketball coach is investigating whether the number of shots taken can be used to predict the mean number of points scored. Assuming the conditions for inference have been met, which of the following inference procedures is the most appropriate to estimate the mean change in the number of points scored for each increase of 1 shot taken? A A one-sample tt-interval for means B A linear regression tt-interval for slope C A two-sample tt-interval for a difference between means D A matched-pairs tt-interval for a mean difference E A two-sample zz-interval for a difference between proportions

B A linear regression tt-interval for slope

A chi-square test for homogeneity was conducted to investigate whether the four high schools in a school district have different absentee rates for each of four grade levels. The chi-square test statistic and pp-value of the test were 19.02 and 0.025, respectively. Which of the following is the correct interpretation of the pp-value in the context of the test? A Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or smaller. B Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger. C Assuming that each high school has a different absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger. D There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is the same. E There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is different.

B Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.

Last year the mean cost μμ for a one-bedroom rental in a certain city was $1,200 per month. Eli is looking for a one-bedroom apartment and is investigating whether the mean cost is less now than what it was last year. A random sample of apartments had a sample mean x¯x¯ of $1,180 per month. Assuming all conditions for inference are met, Eli will conduct a hypothesis test as part of his investigation. Which of the following is the correct set of hypotheses? A H0:μ=1,200Ha:μ>1,200H0:μ=1,200Ha:μ>1,200 B H0:μ=1,200Ha:μ<1,200H0:μ=1,200Ha:μ<1,200 C H0:x¯=1,200Ha:x¯<1,200H0:x¯=1,200Ha:x¯<1,200 D H0:x¯=1,180Ha:x¯≠1,180H0:x¯=1,180Ha:x¯≠1,180 E H0:x¯=1,180Ha:x¯<1,180

B H0:μ=1,200Ha:μ<1,200

At a large university, the division of computing services surveyed a random sample of 45 biology majors and 55 business majors from populations of over 1,000 biology and 1,000 business majors. The sampled students were asked how many hours they spend per week using any university computer lab. Let x¯1x¯1 represent the average hours per week spent in any university computer lab by the 45 biology majors, and let x¯2x¯2 represent the average hours per week spent in any university computer lab by the 55 business majors. Which of the following is the best explanation for why the sampling distribution of x¯1−x¯2x¯1−x¯2 can be modeled with a normal distribution? A The two sample standard deviations are assumed to be equal. B The sample sizes are both sufficiently large. C The distributions of the population are normal. D The population standard deviations are assumed equal. E There are at least 30 students in each of the two populations.

B The sample sizes are both sufficiently large.

From a random sample of potential voters in an upcoming election, 47% indicated they intended to vote for Candidate R. A 95 percent confidence interval was constructed from the sample, and the margin of error for the estimate was 5%. Which of the following is the best interpretation of the interval? A We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%. B We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%. C We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is 47%. D We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47%. E We are confident that 95% of the population intend to vote for Candidate R.

B We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%.

A sociologist will conduct a two-sample tt-test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor's degrees and people with master's degrees. From a random sample of 32 people with a bachelor's degree, the average salary was $55,000 with standard deviation $3,500. From a random sample of 28 people with a master's degree, the average salary was $58,000 with a standard deviation of $4,000. With a null hypothesis of no difference in the means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (master's degree minus bachelor's degree) ? A t=(58,000−55,000)4,00028+3,50032√t=(58,000−55,000)4,00028+3,50032 B t=(58,000−55,000)4,000228+3,500232√t=(58,000−55,000)4,000228+3,500232 C t=(58,000−55,000)4,000228+3,500232−−−−−−−−−−√t=(58,000−55,000)4,000228+3,500232 D t=(58,000−55,000)4,000+3,50028+32√t=(58,000−55,000)4,000+3,50028+32 E t=(58,000−55,000)4,0002+3,500228+32√

B t=(58,000−55,000)4,000228+3,500232√

A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars? A (195−286)±1.9924645+5840−−−−−−−√(195−286)±1.9924645+5840 B (195−286)±1.992462+58245+40−−−−−−√(195−286)±1.992462+58245+40 C (195−286)±1.99246245+58240−−−−−−−−√(195−286)±1.99246245+58240 D (286−195)±1.99246245+58240−−−−−−−−√(286−195)±1.99246245+58240 E (286−195)±1.992462+58245+40−−−−−−√

C (195−286)±1.99246245+58240−−−−−−−−√

The following table shows the probability distribution for the number of books a student typically buys at the annual book fair held at an elementary school. Number of Books01234567Probability0.350.200.150.100.070.080.040.01 Let the random variable BB represent the number of books a student buys at the next book fair. What is the expected value of BB ? A 0 B 1.00 C 1.79 D 3.50 E 28

C 1.79

A private lake sells boating memberships and currently has 600 members. During the application process the potential members are asked which recreational activity they do the most. Their choices are fishing, skiing, boarding, swimming, or tubing. The lake manager chooses clients according to their interests to maximize the use of all areas of the lake. Every month, the lake rangers randomly sample the boats on the lake and categorize them according to the activity they are doing. The lake manager performs a chi-square goodness-of-fit test using the following null hypothesis to see whether their samples differ significantly from what the original applications claim. H0:pfish=0.26,pski=0.21,pboard=0.30,pswim=0.12,ptube=0.11H0:pfish=0.26,pski=0.21,⁢pboard=0.30,⁢pswim=0.12,ptube=0.11 In order to meet the conditions for independence and large counts for a chi-square goodness-of-fit test, which of the following represents all possible sizes of the monthly samples? A n≥30n≥30 B 30≤n≤5030≤n≤50 C 46≤n≤6046≤n≤60 D n≥46n≥46 E n≤60

C 46≤n≤60

For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal? A A random sample of 8 taken from a normally distributed population B A random sample of 50 taken from a normally distributed population C A random sample of 10 taken from a population distribution that is skewed to the right D A random sample of 75 taken from a population distribution that is skewed to the left E A random sample of 100 taken from a population that is uniform

C A random sample of 10 taken from a population distribution that is skewed to the right

Two voting districts, C and M, were sampled to investigate voter opinion about tax spending. From a random sample of 100 voters in District C, 22 percent responded yes to the question "Are you in favor of an increase in state spending on the arts?" An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question. A 95 percent confidence interval for the difference (pc−pm)(pc−pm) was calculated as −0.04±0.12−0.04±0.12. Which of the following is the best interpretation of the interval? A We are 95% confident that the majority of all voters in the state favor an increase in state spending for the arts. B We are 95% confident that less than half of all voters in the state favor an increase in state spending for the arts. C We are 95% confident that the difference in the proportions of all voters in districts C and M who favor an increase in state spending for the arts is between −0.16−0.16 and 0.08. D We are 95% confident that the difference in the sample proportions of voters in districts C and M who favor an increase in state spending for the arts is between −0.16−0.16 and 0.08. E We are 95% confident that the proportion of all voters in the state who favor an increase in state spending for the arts is between −0.16−0.16 and 0.08.

C We are 95% confident that the difference in the proportions of all voters in districts C and M who favor an increase in state spending for the arts is between −0.16−0.16 and 0.08.

Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means. Is the sampling distribution of the difference in sample means approximately normal? A Yes, because Alicia selected a random sample. B Yes, because for each brand it is reasonable to assume that the population size is greater than ten times its sample size. C Yes, because the size of each sample is at least 30. D No, because the distribution of Brand A shoes has outliers. E No, because the shape of the population distribution is unknown.

C Yes, because the size of each sample is at least 30.

In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is 1616. What is the probability that it takes three rolls until the player rolls doubles? A (16)3(16)3 B (56)3(56)3 C (16)(56)3(16)(56)3 D (16)(56)2(16)(56)2 E (56)(16)2

D (16)(56)2(16)(56)2

A seafood festival organizer is interested in whether there is a relationship between the number of ingredients in the clam chowders that are entered in the festival's clam chowder contest and the ratings given to the chowders by the judges. The organizer requires each of the twelve restaurants in the competition to list all of its chowder's ingredients and requires each judge who tastes the clam chowders to rate each chowder from one through ten on a note card. The organizer then randomly selects twenty-five note cards. Assuming that all conditions for inference are met, which of the following significance tests should be used to investigate whether having more ingredients in the chowders is associated with a reduction in the ratings given to the chowders by the judges? A A chi-square test of independence B A two-sample tt-test for a difference between means C A two-sample zz-test for a difference between proportions D A linear regression tt-test for slope E A matched pairs tt-test for a mean difference

D A linear regression tt-test for slope

A factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. The difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. The pp-value of the test was 0.018. Which of the following is the correct interpretation of the pp-value? A If there is a difference of 0.018 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.006. B If there is a difference of 0.006 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.018. C If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.006 is 0.018. D If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at least 0.006 is 0.018. E If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at most 0.006 is 0.018.

D If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at least 0.006 is 0.018

A local arts council has 200 members. The council president wanted to estimate the percent of its members who have had experience in writing grants. The president randomly selected 30 members and surveyed the selected members on their grant-writing experience. Of the 30 selected members, 12 indicated that they did have the experience. Have the conditions for inference with a one-sample zz-interval been met? A Yes, all conditions for inference have been met. B No, because the sample size is not large enough to satisfy the conditions for normality. C No, because the sample was not selected at random. D No, because the sample size is not less than 10 percent of the population size. E No, because the sample is not representative of the population.

D No, because the sample size is not less than 10 percent of the population size.

Which of the following conditions will create a biased estimator of a population parameter? A The sampling distribution of the estimator is skewed to the left. B The sampling distribution of the estimator is skewed to the right. C The sampling distribution of the estimator is not the same shape as the distribution of the population parameter. D The expected value of the estimator is not equal to the population parameter. E The variability of the sampling distribution of the estimator is not equal to the variability of the population parameter.

D The expected value of the estimator is not equal to the population parameter.

Researchers at a medical center studied the amount of caffeine, in milligrams (mg), contained in a 16-ounce cup of coffee made at one machine at the center's cafeteria. They selected a random sample of 40 16-ounce cups of coffee made at different times of the day during a one-month period. The mean and standard deviation of the amount of caffeine in the sample were 159.88 mg and 36.72 mg, respectively. A graph of the sample data revealed a right skew with one outlier. The researchers will construct a confidence interval to estimate the amount of caffeine for all 16-ounce cups made at the machine. Which of the following conditions is not needed for the inference? A The samples were selected at random. B The observations are independent of one another. C The sample size of 40 is less than 10% of the population size. D The graph of the sample data is symmetric with no outliers. E The sample size is large enough to assume that the sampling distribution of sample means is approximately normal.

D The graph of the sample data is symmetric with no outliers.

An agronomist is an expert in soil management and crop production. A certain state hires an agronomist to investigate whether there is a linear relationship between a wheat stalk's height and the yield of wheat. The agronomist collected data and used the data to test the claim that there is a linear relationship at a significance level of α=0.05α=0.05. The agronomist tested the following hypotheses. H0:β1=0Ha:β1≠0H0:β1=0Ha:β1≠0 The test yielded a pp-value of 0.25. Which of the following is a correct conclusion about the claim? A The null hypothesis is rejected because 0.25>0.050.25>0.05. There is sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield. B The null hypothesis is not rejected because 0.25>0.050.25>0.05. There is sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield. C The null hypothesis is rejected because 0.25>0.050.25>0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield. D The null hypothesis is not rejected because 0.25>0.050.25>0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield. E The null hypothesis is accepted because 0.25>0.050.25>0.05. There is sufficient evidence to suggest that there is not a linear relationship between a wheat stalk's height and its yield.

D The null hypothesis is not rejected because 0.25>0.050.25>0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield.

A company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H0:p=0.08H0:p=0.08 versus Ha:p>0.08Ha:p>0.08 at the significance level of α=0.01.α=0.01. The test yielded a pp-value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion? A The pp-value is greater than αα, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. B The pp-value is greater than αα, and the null hypothesis is rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. C The pp-value is greater than αα, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. D The pp-value is less than αα, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. E The pp-value is less than αα, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

D The pp-value is less than αα, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious apples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence? A (-0.076,0.236)(-0.076,0.236) B (-0.105,0.265)(-0.105,0.265) C (-10.5,26.5)(-10.5,26.5) D (-76,236)(-76,236) E (−105,265)(−105,265)

E (−105,265)

Ecologists conducted a study to investigate the potential ecological impact of golf courses. Investigators monitored the reproductive success of bluebirds in birdhouses at nine golf courses and ten similar birdhouses at nongolf sites. Data on nests in birdhouses occupied only by bluebirds are shown in the table. Observed Number of Nests per Birdhouse by Location 0 nests1 nest2 or 3 nestsTotalGolf3042880Nongolf405822120Total7010030200 If the proportions of nests occupied is the same for golf and nongolf sites, what would be the expected count of birdhouses with 1 nest in nongolf locations? A 40 B 42 C 50 D 58 E 60

E 60

A random sample of 500 people were classified by their ages into 3 age-groups: 29 years and younger, 30 to 64 years, and 65 years and older. Each person from the sample was surveyed about which of 4 major brands of cell phone they used. Their responses were compiled and displayed in a 3-by-4 contingency table. A researcher will use the data to investigate whether there is an association between cell phone brand and age-group. Which of the following is the appropriate test for the investigation? A A one-sample tt-test for a population mean B A two-sample tt-test for a difference between means C A chi-square goodness-of-fit test D A chi-square test of homogeneity E A chi-square test of independence

E A chi-square test of independence

A sports equipment researcher investigated how different types of wood used to make baseball bats might affect batting. The researcher selected a sample of 80 batters from summer baseball leagues and randomly assigned the batters to one of two groups: the ash bat group or the maple bat group. The mean number of hits for each group was recorded at the end of the season, and the difference in the sample means was calculated. Which of the following is the appropriate inference procedure for analyzing the results of the investigation? A A one-sample tt-interval for a population mean B A one-sample tt-interval for a sample mean C A matched pairs tt-interval for a mean difference D A two-sample tt-interval for a difference between sample means E A two-sample tt-interval for a difference between population means

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

A veterinarian keeps track of the types of animals treated by an animal clinic. The following distribution represents the percentages of animals the clinic has historically encountered. Animal typeDogsCatsLivestockBirdsOtherPercent61%22%8%6%3% If the animal clinic treats 230 animals in a month, how many of each animal type would be expected? A Animal typeDogsCatsLivestockBirdsOtherExpected6122863 B Animal typeDogsCatsLivestockBirdsOtherExpected1224416126 C Animal typeDogsCatsLivestockBirdsOtherExpected1405118147 D Animal typeDogsCatsLivestockBirdsOtherExpected4646464646 E Animal typeDogsCatsLivestockBirdsOtherExpected140.350.618.413.86.9

E Animal typeDogsCatsLivestockBirdsOtherExpected140.350.618.413.86.9

A company that ships crystal bowls claims that bowls arrive undamaged in 95 percent of the shipments. Let the random variable GG represent the number of shipments with undamaged bowls in 25 randomly selected shipments. Random variable GG follows a binomial distribution with a mean of 23.75 shipments and a standard deviation of approximately 1.09 shipments. Which of the following is the best interpretation of the mean? A Every shipment of 25 bowls will have 23.75 undamaged bowls. B Every shipment of 25 bowls will have 23.75 damaged bowls. C On average, the company receives 23.75 shipments before receiving the first shipment with a damaged bowl. D For all possible shipments of size 25, the average number of damaged shipments is equal to 23.75. E For all possible shipments of size 25, the average number of undamaged shipments is equal to 23.75.

E For all possible shipments of size 25, the average number of undamaged shipments is equal to 23.75.

At a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. A random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of P(x¯>22)≈0.05P(x¯>22)≈0.05? A The probability that each of the 5 backpacks selected will have a weight above 22 pounds is approximately 0.05. B The probability that each of the 5 backpacks selected will have a weight above 19.7 pounds is approximately 0.05. C The probability that the population mean is greater than 22 pounds is approximately 0.05. D For all samples of size 5, approximately 5% of the sample will have a probability greater than 22 pounds. E For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.

E For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.

A reporter responsible for the food section of a magazine investigated the belief that grocery stores sell beef at a higher price in the fall than in the spring. The reporter selected independent random samples of grocery-store beef prices in November and April and computed the mean and standard deviation for the samples. Which of the following are the correct null and alternative hypotheses for the reporter's investigation, where μFμF represents the mean price of beef in the fall and μSμS represents the mean price of beef in the spring? A H0:x¯F−x¯S=0Ha:x¯F−x¯S<0H0:x¯F−x¯S=0Ha:x¯F−x¯S<0 B H0:x¯F−x¯S=0Ha:x¯F−x¯S>0H0:x¯F−x¯S=0Ha:x¯F−x¯S>0 C H0:μF−μS=0Ha:μF−μS≠0H0:μF−μS=0Ha:μF−μS≠0 D H0:μF−μS=0Ha:μF−μS<0H0:μF−μS=0Ha:μF−μS<0 E H0:μF−μS=0Ha:μF−μS>0

E H0:μF−μS=0Ha:μF−μS>0

A baseball enthusiast carried out a simple linear regression to investigate whether there is a linear relationship between the number of runs scored by a player and the number of times the player was intentionally walked. Computer output from the regression analysis is shown. VariableDFEstimateSEIntercept1162.073Intentional Walks10.500.037R-sq=0.63R-sq=0.63 Let β1β1 represent the slope of the population regression line used to predict the number of runs scored from the number of intentional walks in the population of baseball players. A tt-test for a slope of a regression line was conducted for the following hypotheses. H0:β1=0Ha:β1≠0H0:β1=0Ha:β1≠0 What is the appropriate test statistic for the test? A t=162.073t=162.073 B t=160.63t=160.63 C t=160.50t=160.50 D t=0.500.63t=0.500.63 E t=0.500.037

E t=0.500.037

A researcher collected data on the cholesterol level, CC, and the age, AA, of 24 people selected at random. Using the data, the researcher calculated the least-squares regression line to be Cˆ=182+2.2AC^=182+2.2A and the standard error of the slope to be 0.38. If the conditions for inference are met, which of the following is closest to the value of the test statistic to test the hypotheses H0:β=0H0:β=0 versus Ha:β≠0Ha:β≠0 ? A t=0.17t=0.17 B t=0.38t=0.38 C t=0.836t=0.836 D t=2.2t=2.2 E t=5.79t=5.79

E t=5.79t=5.79

In a population of bats living in a certain region, 30 percent have a wingspan greater than 10 inches. In a random sample of 80 bats living outside of the region, 20 had a wingspan greater than 10 inches. Consider a one-sample zz-test to investigate whether there is evidence that the proportion of bats with a wingspan greater than 10 inches living outside the region is different from that of the bats living in the region. Which of the following is the correct test statistic? A z=0.30−0.25(0.25)(0.75)80√z=0.30−0.25(0.25)(0.75)80 B z=0.30−0.25(0.30)(0.70)80√z=0.30−0.25(0.30)(0.70)80 C z=0.20−0.30(0.30)(0.70)80√z=0.20−0.30(0.30)(0.70)80 D z=0.25−0.30(0.25)(0.75)80√z=0.25−0.30(0.25)(0.75)80 E z=0.25−0.30(0.30)(0.70)80√z=0.25−0.30(0.30)(0.70)80

E z=0.25−0.30(0.30)(0.70)80√

The manager of the cafeteria at a local high school wanted to see if there was an association between a student's grade level and whether the student approves of the food choices in the cafeteria. The manager selected a random sample of students and asked if they approved of the food choices and also recorded the grade levels of the students. If a student was in ninth or tenth grade, he or she was labeled as an underclassman, and if the student was in eleventh or twelfth grade, he or she was labeled as an upperclassman. The table shows the results of the survey. UnderclassmanUpperclassmanTotalApproves of the Cafeteria Food502070Does Not Approve of the Cafeteria Food306090Total8080160 Assuming that all conditions for inference have been met, which of the following equations gives the appropriate chi-square test statistic and the correct number of degrees of freedom to determine if there is an association between grade level and whether a student approves of the food choices in the cafeteria? A χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240 with 4 degrees of freedom B χ2=(50−35)250+(20−35)220+(30−45)230+(60−45)260χ2=(50−35)250+(20−35)220+(30−45)230+(60−45)260 with 4 degrees of freedom C χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 4 degrees of freedom D χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240 with 1 degree of freedom E χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 1 degree of freedom

E χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 1 degree of freedom