Free Printable AP Stat Exam Review

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AP Stat Exam Review

Total questions: 50

Worksheet time: 3hrs 49mins

Name

Class

Date

Which of the following is the best estimate of the standard deviation of the distribution in the figure?

106

A company wanted to determine the child care costs of its employees. A sample of 25 employees were interviewed and their child care expenses for the previous year were determined. Later, the company discovered that the highest expense in the sample was mistakenly recorded as 5 times the actual amount. However, after correcting the error, the correct amount was still greater than or equal to any other expense in the sample. Which of the following sample statistics must have remained the same after the correction was made?

standard deviation

mean

mode

range

median

A company determines the mean and standard deviation of the employees' salaries in one year. What is the best description of the standard deviation?

Approximately the median distance between the individual salaries of employees and the mean of every employee's salary.

The amount of money separating the highest salary from the lowest salary when considering the middle 50% of the distribution.

The amount of money separating the highest salary from the lowest salary when considering all employees.

The distance between the salary of an employee and the mean salary of all the employees.

Approximately the mean distance between the individual salaries of employees and the mean of all employees' salaries.

The equation of the LSRL for the points on a scatterplot is ŷ = 5.3-0.23x. What is the residual for the point (5, 4)?

-0.15

0.15

0.62

0.85

The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Bella is at the 87th percentile in height for adult women, then her height, in inches, is closest to

To check the effect of hot temperatures on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a warm car in the sun for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before the breakage is measured on each rubber band, and the mean for the hot bands is compared to the mean for the others. Is this a good experimental design?

No, because the means are not proper statistics for comparison.

No, because more than two brands should be used.

No, because more temperatures should be used.

No, because temperature is confounded with brand.

Yes

Andrea's doctor told her that the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.75. Which of the following is the best interpretation of this standardized score?

Andrea's systolic blood pressure is 175.

Andrea's systolic blood pressure is 1.75 standard deviations above the average systolic blood pressure of women her age.

Andrea's systolic blood pressure is 1.75 above the average systolic blood pressure of women her age

Only 1.75% of women Andrea's age have a higher systolic blood pressure than she does.

Andrea's systolic blood pressure is 1.75 times the average systolic blood pressure of women her age.

The graph shows the distribution of scores of 30 students on a mathematics test. Based on the histogram, which statement must be true?

The lowest test score is 41%.

The highest test score is 100%.

The mean test score is between 81% and 90%.

The median test score is not greater than 80%.

The lower quartile of the test scores is greater than 60%.

At a college the scores on the Spanish final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the Humanities final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the Spanish final and 84 on the Humanities final. Relative to the students in each respective class, in which subject did this student do better?

The student did better in Spanish.

The student did better in Humanities.

There is no basis for comparison, since the subjects are different from each other and are in different departments.

The student did equally well in each course.

There is not enough information for comparison.

10.

In a certain school, students can choose whether to eat in the school’s cafeteria. A reporter working for the school’s newspaper polled students on their reactions to changes in the menu at the cafeteria. For each student leaving the cafeteria in one 20-minute time period, the reporter used a die to determine whether to stop the student and ask how he or she felt about the new menu. In the reporter’s article it was stated that a random sample of the students showed that 23% of the school’s student population was happy with the new menu. Which of the following statements is true?

Because each student leaving the cafeteria was randomly selected and could choose to answer or not, this is a random sample of the student population, and the 23% is an accurate measurement of the school population’s view of the new menu.

Because students self-selected whether to eat in the cafeteria, the sampling method might be biased and the sample might not be representative of all students in the school.

The survey would have been more effective if the reporter had collected the data in one 10-minute time period rather than in one 20-minute time period.

The survey would have been more effective if students who cared about the food could have called the reporter to tell how they felt about the new menu, so that only students with opinions on the subject would have been surveyed.

Because no treatment was imposed on the students eating in the cafeteria, one cannot make any conclusions about the new menu.

11.

The student government at a high school wants to conduct a survey of student opinion. It wants to begin with a simple random sample of 80 students. Which of the following survey methods will produce a simple random sample?

Survey the first 80 students to arrive at school in the morning

Survey every 5th student entering the school library until 80 students are surveyed.

Use random numbers to choose 20 each of first-year, second-year, third-year, and fourth-year students.

Number the students in the official school roster. Use a table of random numbers to choose 80 students from this roster for the survey.

Number the cafeteria seats. Use a table of random numbers to choose seats and interview the students until 80 have been interviewed.

12.

The segmented bar charts below depict the data from the NAAL (National Assessment of Adult Literacy) conducted in 2003. Based on the graph, which statement must be true.

The prose literacy level with the greatest percentage of people who volunteered once per week or more was below basic.

For people with proficient prose literacy level, the number who volunteered once per week or more was greater than the number who volunteered less than once per week.

Intermediate and proficient prose level had the same number of students who volunteered less than once per week.

Of all the students that never volunteered, the greatest number were in the below basic level of prose literacy.

For students who had basic prose literacy level, the number who volunteered less than once per week was greater than those who never volunteered.

13.

The boys and girls basketball teams at a high school had their heights measured at practice. The following data was recorded for their heights. What can you conclude from the distributions?

The girls have a larger median and a larger range in heights.

The boys had a smaller median height than the girls; however, the boys had a larger range of heights.

The median height for the boys and the girls is the same; however, the girls have a larger range.

The median height for the boys is larger; however, the girls have a larger range.

No information can be concluded from the distribution since there is no key included.

14.

A cosmetics supplier ships boxes of highlighter to individual customers. The distribution of weights of shipped boxes is approximately normal with mean 5 pounds and standard deviation 1.2 pounds. Which expression represents the weight, in pounds, at the 75th percentile of the distribution?

-1.96(1.2) + 5

-0.25(1.2) + 5

0.25(1.2) + 5

0.67(1.2) + 5

0.75(1.2) + 5

15.

The boxplots summarize two data sets, 1 and 2. Which of the following must be true?

I. Class #2 contains more data than Class #1.

II. The box of Class #2 contains more data than the box of Class #1.

III. The data in Class #1 has a smaller range than the data in Class #2.

I only

I and III only

I and II only

I, II, and III

III only

16.

What can be used to show a cause-and-effect relationship between two variables?

A controlled experiment

A census

An observational study

A cross-sectional study

A sample survey

17.

Use the table to answer the following question. Of the male subjects in the study, what fraction drive a sports car?

39/84

39/240

39/60

60/240

84/240

18.

The Teachers' Health Study, a large medical experiment involving 18,000 female teachers, attempted to determine whether aspirin could help prevent heart attacks. In this study, one group of about 9,000 teachers took an aspirin every other day, while a control group took a placebo. After several years, it was determined that the teachers in the group that took aspirin had significantly fewer heart attacks than the teachers in the control group. Which of the following statements explains why it would not be appropriate to say that everyone should take an aspirin every other day?

I. The study included only teachers, and different results may occur in individuals in other occupations.

II. The study included only females and there may be different results with males.

III. Although taking aspirin may be helpful in preventing heart attacks, it may be harmful to some other aspects of health.

I only

II only

II and III only

I and III only

I, II, and III

19.

What is the inter-quartile range for these data?

20.

What's the appropriate interpretation of the slope of the regression line?

For every additional 0.61 hours of growth, the culture is predicted to weight 1 more gram.

For every additional hour of growth, the culture is predicted to weigh 0.61 more grams.

For every additional hour of growth, the logarithm of the culture's weight in grams is predicted to increase by 0.61.

At the beginning of the experiment, the logarithm of the culture's weight in grams was approximately 0.61 ounces.

21.

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

Ho: p=.21
Ha: p > .21

Ho: p< .21
Ha: p= .21

Ho: p> .21
Ha: p= .21

Ho: p= .21
Ha: p< .21

22.

5% of trucks of a certain model have needed new engines after being driven between 0 and 100 miles. The manufacturer hopes that the redesign of one of the engine's components has solved this problem. Write the null and alternative hypotheses for this situation.

Ho: p< 0.05
Ha: p = 0.05

Ho: p = 0.05
Ha: p > 0.05

Ho: p = 0.05
Ha: p < 0.05

Ho: p > 0.05
Ha: p = 0.05

23.

The probability of observing a value for a test statistic at least as far from the hypothesized value as the statistic value actually observed if the null hypothesis is true is called...

P-Hat

One-Proportion z-test

P-Value

24.

A Type I error is when:

We obtain the wrong test statistic

We reject the null hypothesis when it is actually true

We fail to reject the null hypothesis when it's actually false

We reject the alternate hypothesis when it's actually true

25.

The measure of the strength, direction and form of the association can be measured by:

r²

correlation

linear regression

26.

To test a claim about a mean, when the population standard deviation is unknown we use:

z procedures

Pythagorean Theorem

t procedures

np > 10 and n(1-p) > 10

27.

A friend has placed a large number of plastic disks in a hat and invited you to select one at random. He informs you that half are red and half are blue. If you draw a disk, record the color, replace it, and repeat 100 times, which of the following is true?

It is unlikely you will choose red more than 50 times.

If you draw 10 blue disks in a row, it is more likely you will draw a red on the next try.

The overall proportion of red disks drawn should be close to 0.50.

The chance that the 100th draw will be red depends on the results of the first 99 draws.

28.

People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population has O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor?

0.280

0.526

0.720

29.

A die is loaded so that the number 6 comes p three times as often as any other number. What is the probability of rolling a 4, 5, or 6?

2/3

1/2

5/8

1/3

30.

A dealer in Las Vegas selects 10 cards from a standard deck of 52 cards. Let Y be the number of diamonds in the 10 cards selected. Which of the following best describes this setting?

Y has a binomial distribution with n = 10 observations and probability of success p = 0.25.

Y has a binomial distribution with n = 10 observations and probability of success p = 0.25, provided the deck is shuffled well.

Y is a binomial distribution with n = 10 observations and probability of success p = 0.25, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

Y has a geometric distribution with n = 10 observations and probability of success p = 0.25

31.

It is known that about 90% of the widgets made by Buckley Industries meet specifications. Every hour a sample of 18 widgets is selected at random for testing and the number of widgets that meet specifications is recorded. What is the approximate mean and standard deviation of the number of widgets meeting

μ = 1.62; σ = 1.414

μ = 1.62; σ = 1.265

μ = 16.2; σ = 1.62

μ = 16.2; σ = 1.273

32.

Le the random variable X represent the amount of money Carl makes tutoring statistics students in the summer. Assume that X is Normal with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected summer, Carl will make less than about

$144

$216

$255

$30

33.

The time it takes students to complete a statistics quiz has a mean of 20.5 minutes and a standard deviation of 15.4 minutes. What is the probability that a random sample of 40 students will have a mean completion time greater than 25 minutes?

0.9678

0.0322

0.0344

0.3851

34.

A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed 60 times. The probability that more than 1/3 of the tosses are heads is closest to

0.9951

0.33

0.109

0.09

35.

The incomes in a certain large population of college teachers have a normal distribution with mean $60,000 and standard deviation $5000. Four teachers are selected at random from this population to serve on a salary review committee. What is the probability that their average salary exceeds $65,000?

0.0228

0.1587

0.8413

0.9772

36.

I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean of the population. Which of the following would produce a wider confidence interval, based on these same data?

Use a larger confidence level

Use a smaller confidence level

Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger

Increase the sample size

37.

You are told that the proportion of those who answered "yes" to a poll about internet use is 0.70, and that the standard error is 0.0459. The sample size is

100

200

38.

The standardized test scores of 16 students have mean x̄ = 200 and standard deviation s = 20. What is the standard error of x̄?

1.25

39.

After a college's football team once again lost a football game to the college's arch rival, the alumni association decided to conduct a survey to see if alumni were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach. Which of the following is the smallest sample size needed to guarantee an estimate that's within 0.05 of p at a 95% confidence level?

269

385

538

768

40.

A claimed psychic was presented with 200 cards face down and asked to determine if the card was one of five symbols: a star, cross, circle, square, or three wavy lines. The "psychic" was correct in 50 cases. To determine if he has ESP, we test the hypothesis H₀: p = 0.20, Hₐ: p > 0.20, where p represents the true proportion of cards for which the psychic would correctly identify the symbol in the long run. Assume the conditions for inference are met. The P-value is

between .10 and .05

between .05 and .025

between .025 and .01

between .01 and .001

41.

A medical researcher wishes to investigate the effectiveness of exercise versus diet in losing weight. Two groups of 25 overweight adult subjects are used, with a subject in each group matched to a similar subject in the other group on the basis of a number of physiological variables. One of the groups is placed on a regular program of vigorous exercise but with no restriction on diet, and the other is placed on a strict diet but with no requirement to exercise. The weight losses after 20 weeks are determined for each subject, and the difference between matched pairs of subjects (weight loss of subject in exercise group - weight loss of matched subject in diet group) is computed. The mean of these differences in weight loss is found to be 2 lb with standard deviation sₓ = 4 lb. Is this convincing evidence of a difference in mean weight loss for the two methods? To answer this question, you should use

one-proportion z test

one-sample z interval for μₓ

one-proportion z interval

one-sample t test for μₓ

42.

An SRS of 100 teachers showed that 64 owned smartphones. An SRS of 100 students showed that 80 owned smartphones. Let pₑ be the proportion of all teachers who own smartphones, and let pₓ be the proportion of all students who own smartphones. A 95% confidence interval for the difference pₑ - pₓ is

(0.264, 0.056)

(0.098, 0.222)

(-0.222, -0.098)

(-0.283, -0.038)

43.

If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)?

0.1248

0.28

0.6352

0.76

44.

In your top dresser drawer are 6 blue socks and 10 grey socks, unpaired and mixed up. One dark morning you pull two socks from the drawer (without replacement, of course!) What is the probability that the two socks match?

0.075

0.375

0.450

0.500

45.

A simple random sample of 1000 Americans found that 62% were satisfied with the service provided by the dealer from which they bought their car. A simple random sample of 1000 Canadians found that 59% were satisfied with the service provided by the dealer from which they bought their car. The sampling variability associated with these statistics is

exactly the same

not exactly the same, but very close

much smaller for the sample of Canadians because the population of Canad is much smaller than that of the United States, hence the sample is a larger proportion of the population.

smaller for the sample of Canadians because the percent satisfied was smaller than that of Americans.

46.

When conducting a significance test for the difference in proportions, why do we pool the data when finding standard error?

Because we like to swim

Because we assume p1 = p2 in Ho

Because the sample sizes are always equal

To be safe and make sure we don't underestimate the standard error

Because we don't the standard deviation.

47.

When creating a confidence interval for the difference of 2 proportions, we pool the samples when finding standard error

True

False

48.

What do we use to estimate unknown parameters?

Hypothesis Test

Confidence Interval

Trig Identity

Guess and check

49.

White blood cell counts are normally distributed with mean 7500 and variance 500. If a patient has taken 50 laboratory blood tests that have a mean of 6899.75 and a standard deviation of 393.44, does this give evidence that his white blood cell count is significantly different than normal?

One-Sample T Test for a Mean

One-Sample Z Test for a Proportion

One-Sample Z Test for a Mean

One-Sample T Test for a Proportion

50.

In 1975, a random sample of 1484 adult U.S. citizens was surveyed, and 193 strongly agreed with the statement, "People should take care of themselves". Then, in 1991, a survey of 1013 adult U.S. citizens showed that only 61 strongly agreed with the statement. Does this indicate that the proportion of U.S.adults who strongly agree with the given statement has dropped?

Two-Sample Z Test for the Difference in Proportions

Two-Sample T Test for the Difference in Means

Matched Pairs T Test for a Mean

One-Sample T Test for a Mean

100 %

AP Stat Exam Review

Total questions: 50

Worksheet time: 3hrs 49mins

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