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. Which of the following hypotheses should the company test?

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 survey was conducted in which both men and women were asked a question about a current issue. Possible responses to this question were “in favor of,” “not in favor of,” or “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

If a probability distribution is symmetric, which of the following statements must be true?

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?

Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months. A random sample of children will be selected, and the age at which each child begins to walk will be recorded. A 99 percent confidence interval for the average age at which children begin to walk will be constructed using the data obtained from the sample of children. Of the following, which is the smallest sample size that will result in a margin of error of 0.1 month or less for the confidence interval?

Let X be a random variable that has a skewed distribution with mean µ = 10 and standard deviation σ = 10. Based on random samples of size 400, the sampling distribution mean is

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. Which of the following statements is true?

Makers of a new pain-relieving medication claim that it relieves chronic pain faster than the current top-selling pain reliever on the market. A double-blind experiment was conducted in which 10 people who experience chronic pain were randomly selected to take either the new or the current medication. Each of the 10 people recorded the time, in minutes, from taking the medication until pain relief. After an appropriate time period, each of the 10 people took the other medication and recorded the time from taking the medication until pain relief. The medication each person took first was randomly determined, and because both medications look the same, the people in the study did not know which medication was taken first. The table shows summary statistics for the results. Which of the following values is closest to the p-value of the appropriate t-test?

Which of the following graphs represents a binomial distribution with n = 20 and p = 0.25?

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 outcome, 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 police officer is using a radar device to check motorists’ speeds. Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. Assuming that the police officer’s estimate is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?

Zucchini weights are approximately normally distributed with mean 0.8 pound and standard deviation

0.25 pound. Which of the following shaded regions best represents the probability that a randomly selected zucchini will weigh between 0.55 pound and 1.3 pounds?

In a recent survey, high school students and their parents were asked to rate 60 recently released movies. The ratings were on a scale from 1 to 9, where 1 was “horrible” and 9 was “excellent”. For each movie, the average rating by the students and the average rating by their parents was calculated and the scatterplot was constructed. The horizontal axis represents the student rating, and the vertical axis represents the parent rating. Thus, an individual data point would represent the rating of a single movie. Which of the following statements is justified by the scatterplot?

Jessica wanted to determine if the proportion of males for a certain species of laboratory animal is less than 0.5. She was given access to appropriate records that contained information on 12,000 live births for the species. To construct a 95 percent confidence interval, she selected a simple random sample of 100 births from the records and found that 31 births were male.

Based on the study, which of the following expressions is an approximate 95 percent confidence interval estimate for p, the proportion of males in the 12,000 live births?

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?

Dan selected a random sample of 100 students from the 1,200 at his school to investigate preferences for making up school days lost due to emergency closings. The results are shown in the table. Dan incorrectly performed a large sample test of the difference in two proportions using 58/100 and 42/100 and calculated a p-value of 0.02. Consequently, he concluded that there was a significant difference in preference for the two options. Which of the following best describes his error in the analysis of these data?

The figure summarizes the heights, in centimeters, of approximately 400 pine seedlings six years after they were planted at a center for environmental study. Approximately half of the trees were fertilized yearly, and the remaining trees were never fertilized. Which of the following statements about the medians and interquartile ranges (IQRs) of the heights of the two groups of trees 6 years after being planted is true?

In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course?

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?

Two friends, Andy and Bob, participate in a game of bowling every week. From past experiences, it is known that both friends’ scores are approximately normally distributed, where Andy has a mean score of 150 with a standard deviation of 30, and Bob has a mean score of 165 with a standard deviation of 15. Assuming that their scores are independent, which of the following values is closest to the probability that Andy will have a greater score than Bob in a single game?

Scientists have long believed that linear regression could be used to predict the brain weight of nonhuman mammals from the body weight. In one study, body weight, in kilograms, and brain weight, in grams, of 22 nonhuman mammals were measured. A linear regression analysis was performed, yielding the output as seen. Assuming that all conditions for inference are met, which of the following expressions represents a 95 percent confidence interval for the slope of the least squares regression line?

A certain motel is roughly 20 miles from the entrance to Yosemite National Park. 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 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?

The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aliyaah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aliyaah’s height, and how does her height compare to Jayne’s height?

For the three histograms, which of the following correctly orders the histograms from the one with the smallest proportion of data above its mean to the one with the largest proportion of data above its mean?

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?

The weight, in pounds, of a full backpack and the corresponding number of books in the backpack were recorded for each of 10 college students. The resulting data were used to create the residual plot and the regression output is shown. Which of the following values is closest to the actual weight, in pounds, of the backpack for the student who had 4 books in the backpack?

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 be selected from 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 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 group of students wanted to investigate the claim that the average number of text messages sent yesterday by students in their school was greater than 100. They asked each student in a random sample of 50 students how many text messages he or she sent yesterday. An appropriate t-test was conducted and resulted in a p-value of 0.0853. Assuming the conditions for the t-test were met, which of the following is an appropriate conclusion?

Two college roommates have each committed to donating to charity each week for the next year. The roommates’ weekly incomes are independent of each other. Suppose the amount donated in a week by one roommate is approximately normal with mean $30 and standard deviation $10, and the amount donated in a week by the other roommate is approximately normal with mean $60 and standard deviation $20. Which of the following is closest to the expected number of weeks in a 52-week year that their combined donation will exceed $120 ?

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 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?

Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6 ?

A study compared the language skills and mental development of two groups of 24-month-old children.

One group consisted of children identified as talkative, and the other group consisted of children identified as quiet. The scores for the two groups on a test that measured language skills are shown in the table. Assuming that it is reasonable to regard the groups as simple random samples and that the other conditions for inference are met, what statistical test should be used to determine if there is a significant difference in the average test score of talkative and quiet children at the age of 24 months?

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?