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

The mean of the distribution is equal to the median of the distribution.

The interquartile range of the distribution is equal to the standard deviation of the distribution.

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

approximately normal with mean 10 and standard deviation 0.5

highly skewed with mean 10 and standard deviation 10

highly skewed with mean 10 and standard deviation 5

highly skewed with mean 10 and standard deviation 0.5

approximately normal with mean 10 and standard deviation 10

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?

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.

The smallest observation is 12 and it is an outlier. No other observations in the data set could be outliers.

The largest observation is 24 and it is an outlier. No other observations in the data set could be outliers.

Both 12 and 24 are outliers. It is possible that there are also other outliers.

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.

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?

The child will know whether he or she used flash cards or the computer.

The experimenter will know whether the child is a boy or a girl and whether he or she used flash cards or the computer.

The child will know whether he or she is a boy or a girl.

The person who grades the tests will know whether the child was a boy or a girl.

The person who grades the tests will know whether the child used flash cards or the computer.

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?

The movies that the students liked the best also tended to be the movies that the parents liked the best, but the students tended to give higher scores.

The movies that the students liked the best also tended to be the movies that the parents liked the best, but the students tended to give lower scores.

The movies that the students liked the best also tended to be the movies that the parents liked the best, but each group tended to give the same scores.

The movies that the students liked the best tended to be the movies that the parents liked the least, but the students tended to give lower scores.

The movies that the students liked the best tended to be the movies that the parents liked the least, but the students tended to give higher scores.

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 chi-square goodness-of-fit test

A two-sample t -test for a difference of means

A matched-pairs t -test for means

A chi-square test of association

A t -test for a correlation of 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?

A one-sample test for a proportion should have been performed because only one sample was used.

No statistical test was necessary because 0.58 is clearly larger than 0.42.

The results of the test were invalid because less than 10% of the population was sampled.

Dan performed a two-tailed test and should have performed a one-tailed test.

More options should have been included, and a chi-square test should have been performed.

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?

The median for the unfertilized trees is less than the median for the fertilized trees, and the IQR is greater for the unfertilized trees.

The medians and IQRs are the same for the unfertilized trees and the fertilized trees.

The median for the unfertilized trees is greater than the median for the fertilized trees, and the IQR is also greater for the unfertilized trees.

The median for the unfertilized trees is the same as the median for the fertilized trees, and the IQR is greater for the unfertilized trees.

The median for the unfertilized trees is less than the median for the fertilized trees, and the IQR is less for the unfertilized trees.

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?

In repeated sampling, the method produces intervals that include the population mean approximately 95 percent of the time.

In this population, about 95 percent of all rental prices are between $815 and $825.

In this sample, about 95 percent of the 100 rental prices are between $815 and $825.

In repeated sampling, the method produces intervals that include the sample mean approximately 95 percent of the time.

There is a probability of 0.95 that the true mean is between $815 and $825.

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?

The actual distance should be considered a variable, and taking five measurements allows the manager to estimate the variability in the actual distance.

Odometer reading should be considered a variable when used to measure this distance.

The median of the five measurements is more likely to be close to the actual distance than is a single measurement.

If one or two odometers give inaccurate readings, the estimate still should be fairly close to the actual distance.

The manager can get some indication of how far off the estimate might be.

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 more that men and women differ in their color preferences, the larger the chi-square statistic will be.

The null hypothesis for the test is that the proportion of each gender who prefer each color scheme is ⅓.

The sample size is too small to detect a significant difference in a chi-square test for homogeneity of proportions.

The test is not valid because the sample sizes are not equal.

The test would also be appropriate if 90 married couples had been used for the two samples.

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?

Aliyaah’s height is at the 83rd percentile of the distribution, and she is shorter than Jayne.

Aliyaah’s height is at the 17th percentile of the distribution, and she is shorter than Jayne.

Aliyaah’s height is at the 67th percentile of the distribution, and she is shorter than Jayne.

Aliyaah’s height is at the 67th percentile of the distribution, and she is taller than Jayne.

Aliyaah’s height is at the 83rd percentile of the distribution, and she is taller than Jayne.

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?

All three histograms have the same proportion of data above their respective means.

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?

There is an association between cell phone use and accidents, but not necessarily a causal relationship.

Cell phone use increases the likelihood of a car accident.

There is a correlation between cell phone use and accidents, but not necessarily an association.

The association between cell phone use and accidents is negative.

Cell phone use causes more accidents in Canada, but not necessarily in the United States.

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?

To decrease the variability in estimates of the mean commuting time

To remove bias when estimating the proportion of working adults living in urban, suburban, and rural areas

To remove bias when estimating the mean commuting time

To reduce bias when estimating the mean commuting time

To decrease the variability in estimates of the proportion of working adults living in urban, suburban, and rural areas

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?

Participants within each block should be as similar as possible with respect to how easily they get sunburned.

Participants in the same block should receive the same lotion.

Participants should be randomly assigned to the blocks.

Participants should be kept blind as to which block they are in.

Participants within each block should be as different as possible with respect to how easily they get sunburned.

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?

Because p > 0.05, at the 5% significance level, it cannot be concluded that the mean number of text messages sent yesterday by students in the school is greater than 100.

Because p < 0.10, at the 10% significance level, it can be concluded that the mean number of text messages sent yesterday by students in the school is less than 100.

Because p < 0.10, at the 10% significance level, it cannot be concluded that the mean number of text messages sent yesterday by students in the school is greater than 100.

Because p > 0.05, at the 5% significance level, it can be concluded that the mean number of text messages sent yesterday by students in the school is greater than 100.

Because p > 0.05, at the 5% significance level, it can be concluded that the mean number of text messages sent yesterday by students in the school is less than 100.

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 ?

0; the combined donation never exceeds $120 in a week

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?

The sample size is n = 1000, and 50 percent of all students use the vending machines.

The sample size is n = 750, and 20 percent of all students use the vending machines.

The sample size is n = 750, and 25 percent of all students use the vending machines.

The sample size is n = 1000, and 25 percent of all students use the vending machines.

The sample size is n = 500, and 50 percent of all students use the vending machines.

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?

A chi-square goodness-of-fit test

A chi-square test of independence

A matched-pairs t -test for means

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?

The distributions of weight loss of the two treatments are approximately normally distributed.

The sample size is greater than or equal to 10 percent of the population size.

Each of the two groups has at least 5 successes and at least 5 failures.

The volunteers in the supplement group are paired with volunteers in the placebo group.

The expected number of people who lose weight in each group is at least 5.

AP Statistics - 2013

Authored by Matthew Holmes

Mathematics

11th Grade - University

CCSS covered

Used 140+ times

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Height, in meters, is 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?

The mean of the height measurements

The median of the height measurements

The standard deviation of the height measurements

The maximum of the height measurements

The z-scores of the height measurements

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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 stratified random sample

A simple random sample

A cluster sample

A convenience sample

A systematic sample

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?

740 mg to 780 mg

700 mg to 740 mg

680 mg to 720 mg

660 mg to 700 mg

620 mg to 660 mg

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?

H₀: The mean life of Brand B is 1,000 hours.

H₁: The mean life of Brand B is more than 1,000 hours

H₀: The mean life of Brand B is 1,000 hours.

H₁: The mean life of Brand B is less than 1,000 hours

H₀: The mean life of Brand A is 1,000 hours.

H₁: The mean life of Brand A is more than 1,000 hours

H₀: The mean life of Brand A is 1,000 hours.

H₁: The mean life of Brand A is less than 1,000 hours

H₀: The mean life of Brand A is equal to the mean life of Brand B bulbs

H₁: The mean life of Brand A is not equal to the mean life of Brand B bulbs

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The amount of time required for each of 100 mice to navigate through a maze was recorded. The histogram below shows the distribution of times, in seconds, for the 100 mice. Which of the following values is closest to the standard deviation of the 100 times?

2.5 seconds

10 seconds

20 seconds

50 seconds

90 seconds

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

The mean is greater than the median.

The median is the average of the first quartile and the third quartile.

There are fewer selling prices between the first quartile and the median than there are between the median and the third quartile.

There are more selling prices that are less than the mean than selling prices that are greater than the mean.

The value of maximum minus third quartile is less than the value of first quartile minus minimum.

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

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