Statistics

let X represent the number on the face that lands up when a fair six-sided number cube is tossed. the expected value of X is 3.5, and the standard deviation of X is approximately 1.708. two fair six-sided number cubes will be tossed, and the numbers appearing on the faces that land up will be added. which of the following values is closest to the standard deviation of the resulting sum? a. 1.708 b. 1.848 c. 2.415 d. 3.416 e. 5.835

C

Height, in meters, in measured for each person in a sample. After the data are collected, all the height measurements are converted from meters to centimeters by multiplying each measurement by 100. Which of the following statistics will remain the same for both units of measure? A. the mean of the height measurements B. the median of the height measurements C. the standard deviation of the height measurements D. the maximum of the height measurements E. the z-scores of the height measurements

E

a graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph? A. the mean is greater than the median B. the median is the average of the first quartile and the third quartile C. there are fewer selling prices between the first quartile and the median than there are between the median and the third quartile D. there are more selling prices that are less than the mean than selling prices that are greater than the mean E. the value of maximum minus third quartile is less than the value of first quartile minus minimum

E

a recent study examined 699 car accidents in toronto over a fourteen-month period. records of phone service providers were used to determine whether the driver was using a cell phone during or immediately before the accident. overall, the researchers found that drivers using cell phones were 4.3 times as likely to have an accident as drivers who were not using cell phones. the result was statistically significant. which of the following can be concluded from this study? a. cell phone use increases the likelihood of a car accident b. there is an association between cell phone use and accidents, but not necessarily a causal relationship c. there is a correlation between cell phone use and accidents, but not necessarily an association d. the association between cell phone use and accidents is negative e. cell phone use causes more accidents in canada, but not necessarily in the usa

b

a certain motel is roughly 20 miles from the entrance to yosemite national parl. the motel manager wants to get a better estimate of the distance and asks five people to each measure the distance, to the nearest tenth of a mile, using the odometer in his or her car. the manager will use the median of the five measurements as the estimate of the distance. which of the following statements is not a statistical justification for the manager's plan? a. odometer reading should be considered a variable when used to measure this distance b. the median of the five measurements is more likely to be close to the actual distance than is a single measurement c. the actual distance should be considered a variable, and taking five measurements allows the manager to estimate the variability in the actual distance d. if one or two odometers give inaccurate readings, the estimate still should be fairly close to the actual distance e. the manager can get some indication of how far off the estimate might be

c

an experiment will be conducted to determine whether children learn their multiplication facts better by practicing with flash cards or by practicing on a computer. children who volunteer for the experiment will be randomly assigned to one of the two treatments. because the children's gender may affect the outcomes, there will be blocking by gender. after practice, the children will be given a test on their multiplication facts. why will it be impossible to conduct a double-blind experiment? a. the experimenter will know whether the child is a boy or a girl and whether he or she sued flash cards or the computer b. the child will know whether he or she is a boy or a girl c. the child will know whether he or she used flash cards or the computer d. the person who grades the tests will know whether the child was a boy or a girl e. the person who grades the test will know whether the child used flash cards or the computer

c

an experiment will be conducted to test the effectiveness of a weight loss supplement. volunteers will be randomly assigned to take either the supplement or a placebo for 90 days, with 12 volunteers in each group. the subjects will not know which treatment they receive. at the end of the experiment, researchers plan to calculate the mean weight loss for each of the two groups and to construct a two-sample t-confidence interval for the difference of the two treatment means. which of the following assumptions is necessary for the confidence interval to be valid? a. the sample size is greater than or equal to 10 percent of the population size b. each of the two groups has at least 5 successes and at least 5 failures c. the distributions of weight loss of the two treatments are approximately normally distributed d. the volunteers in the supplement group are paired with volunteers in the placebo group e. the expected number of people who lose weight in each group is at least 5

c

monthly rent was determined for each apartment in a random sample of 100 apartments. the sample mean was $820 and the sample standard deviation was $25. an approximate 95 percent confidence interval for the true mean monthly rent for the population of apartments from which this sample was selected is ($815, $825). Which of the following statements is a correct interpretation of the 95 percent confidence level? a. in this population, about 95 percent of all rental prices are between 815 and 825 b. in this sample, about 95 percent of the 100 rental prices are between 815 and 825 c. in repeated sampling, the method produces intervals that include the population mean approximately 95 percent of the time d. in repeated sampling, the method produces intervals that include the sample mean approximately 95 percent of the time e. there is a probability of .95 that the true mean is between 815 and 825

c

a marketing research consultant for a hotel chain hypothesizes that men and women differ in their color preference for guest rooms. the consultant shows pictures of rooms decorated with three different color schemes to each person in a random sample of 110 men and to each person in a random sample of 90 women. the consultant asks each person to choose his or her favorite color scheme. a chi-square test for homogeneity of proportions will be used to test the consultant's hypothesis. assuming that the conditions for inference are met, which of the following statements is true for the test? a. the null hypothesis for the test is that the proportion of each gender who prefer each color scheme is 1/3 b. the sample size is too small to detect a significant difference in a chi-square test for homogeneity of proportions c. the test is not valid because the sample sizes are not equal d. the more that men and women differ in their color preferences, the larger the chi-square statistic will be e. the test would also be appropriate if 90 married couples had been used for the two samples

d

a randomized block design will be used in an experiment to compare two lotions that protect people from getting sunburned. which of the following should guide the formation of the blocks? a. participants in the same block should receive the same lotion b. participants should be randomly assigned to the blocks c. participants should be kept blind as to which block they are in d. participants within each block should be as similar as possible with respect to how easily they get sunburned e. participants within each block should be as different as possible with respect to how easily they get sunburned

d

a town manager is interested in comparing requests for various town-provided services (such as street maintenance and garbage pickup) with nationally published proportions of requests for the same services. each request in a random sample of 500 service requests from the town was classified into one of 10 different categories. which of the following tests could be used to determine whether the proportions of service requests classified into the 10 service categories for the town differ from national proportions? a. a two-sample t-test for a difference of means b. a matched-pairs t-test for means c. a chi-square test of association d. a chi-square goodness-of-fit test e. a t-test for a correlation of proportions

d

if a probability distribution is symmetric, which of the following statements must be true? a. the distribution is normal b. the distribution is uniform c. the distribution is bimodal d. the mean of the distribution is equal to the median of the distribution e. the interquartile range of the distribution is equal to the standard deviation of the distribution

d

a regional transportation authority is interested in estimating the mean number of minutes working adults in the region spend commuting to work on a typical day. a random sample of working adults will beselected form each of three strata: urban, suburban, and rural. selected individuals will be asked the number of minutes they spend commuting to work on a typical day. why is stratification used in this situation? a. to remove bias when estimating the proportion of working adults living in urban, suburban, and rural areas b. to remove bias when estimating the mean commuting time c. to reduce bias when estimating the mean commuting time d. to decrease the variability in estimates of the proportion of working adults living in urban, suburban, and rural areas e. to decrease the variability in estimates of the mean commuting time

e

a university will add fruit juice vending machines to its classroom buildings if the student body president is convinced that more than 20 percent of the students will use them. a random sample of n students will be selected and asked whether or not they would use the vending machines. a large-sample test for proportions at the significance level of alpha=0.05 will be performed. the null hypothesis that the proportion of all students who would use the vending machines is 20 percent will be tested against the alternative that more than 20 percent of all students would use them. for which of the following situations would the power of the test be highest? a. the sample size is n=750 and 20 percent of all students use the vending machines b. the sample size is n=750 and 25 percent of all students use the vending machines c. the sample size is n=1000, and 25 percent of all students use the machines d. the sample size is n=500, and 50 percent of the students use the machines e. the sample size is n=1000 and 50 percent of all students use the vending machines

e

the number of hurricanes reaching the east coast of the united states was recorded for each of the last ten decades by the national hurricane center. summary measures are shown below. min=12 lower quartile=15 median=16 max=24 upper quartile=18 n=10 a. the smallest observation is 12 and it is an outlier. no other observations in the data set could be outliers b. the largest observation is 24 and it is an outlier. no other observations in the data set could be outliers. c. both 12 and 24 are outliers. it is possible that there are also other outliers d. 12 is an outlier and it is possible that there are other outliers at the low end of the data set. there are no outliers at the high end of the data set e. 24 is an outlier and it is possible that there are other outliers at the high end of the data set. there are no outliers at the low end of the data set

e

a school principal wanted to investigate student opinion about the food served in the school cafeteria. the principal selected at random samples of 50 first-year students, 50 second-year students, 50 third-year students, and 50 fourth-year students to complete a questionnaire. Which of the following best describes the principal's sampling plan? A. a stratified random sample B. a simple random sample C. a cluster sample D. a convenience sample E. a systematic sample

A

a candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with mean 720 milligrams (mg). If the manager's belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights? A. 740 mg to 780 mg B. 700 mg to 740 mg C. 680 mg to 720 mg D. 660 mg to 700 mg E. 620 mg to 660 mg

B

a survey was conducted in which both men and women were asked a question about current issue. possible responses to this question were "in favor of", "not in favor of" "no opinion". A chi-square test is to be used to determine whether the response to this question is independent of gender. the number of degrees of freedom for the chi-square test in this situation is a. 6 b. 5 c.3 d.2 e.1

D

a company currently uses Brand A lightbulbs, which have a mean life of 1,000 hours. a salesperson marketing Brand B, a new brand of bulb, contacts the company. the company will switch to the new brand of bulb only if there is convincing evidence that the mean life of Brand B is greater than 1,000 hours. What should the hypotheses for the company test be?

Ho: the mean life of Brand B is 1,000 hours Ha: the mean life of Brand B bulbs is more than 1,000 hours

let X be a random variable that has a skewed distribution with mean u=10 and standard deviation sigma=10. based on random samples of size 400, the sampling distribution of x is a. highly skewed with mean 10 and standard deviation 10 b. highly skewed with mean 10 and standard deviation 5 c. highly skewed with mean 10 and standard deviation .5 d. approximately normal with mean 10 and standard deviation 10 e. approximately normal with mean 10 and standard deviation .5

e