Part I: Multiple Choice

Review for Chapters 1, 2, and 3

1.   A survey to determine the types of calculators used by a statistics class will collect ____ data.

a.    qualitative

b.    discrete

c.    bivariate

d.   continuous

2.   A survey to determine the level of carbon monoxide in your home will collect _____ data.

a.    qualitative

b.    discrete

c.    bivariate

d.   continuous

3.   A survey to determine the number of cell phone chargers one owns will collect _____ data .

a.    qualitative

b.    discrete

c.    bivariate

d.   continuous

4.   A state government is considering the introduction of an item on the next state ballot that would  authorize raising the sales tax 0.5 percent throughout the state in order to help fund new state      roads and for the renovation and maintenance of pre-existing roads. A local newspaper is                conducting a survey of residents throughout the state to assess their support for such an increase. What is the population of interest?

a.    All residents who drive in the state

b.   All registered voters

c.    All residents of the state

d.   All registered voters who shop

e.   All registered voters who drive

5.    In doing an investigation for health care coverage in a metropolitan area, some three-block     neighborhoods are randomly selected. A researcher surveys every head of household in those selected neighborhoods. This is an example of:

a.    Random sampling

b.    Cluster sampling

c.    Systematic sampling

d.    Proportional sampling

e.    Stratified sampling

6.   ABC High School needs to randomly select 200 from a list of students for a state exam in order to continue to receive state funding. This is an example of:

a.    Simple random sampling

b.   Stratified sampling

c.    Cluster sampling

d.   Systematic sampling

7.   ABC High School needs to randomly select 200 students for a state exam in order to continue to      receive state funding.  In order to meet the requirement, school administrators decide to randomly select 10 students from each of 20 homerooms.  This is an example of:

a.    Simple random sampling

b.   Stratified sampling

c.    Cluster sampling

d.   Systematic sampling

8.   ABC High School needs to randomly select 200 students for a state exam in order to continue to        receive state funding.  In order to meet the requirement, school administrators use their                     alphabetical database to select every 5th student beginning with the randomly chosen 6th student on the list until they had 200 students.  This is an example of:

a.    Simple random sampling

b.   Stratified sampling

c.    Cluster sampling

d.   Systematic sampling

9.   Which of the following sampling method(s) is more likely to result in sampling bias?

I.       Convenience sampling

II.       Stratified sampling

III.       Volunteer sampling

a.    I only

b.    II only

c.    III only

d.    I and III

e.    I, II, and III

10. Liza scored at the 85th percentile on the SAT. This means that:

a.    Liza answered 85% of the questions correctly.

b.    Liza scored the same as or higher than 85% of other people who took that same exam.

c.    Eighty-five percent of other people who took the same exam scored higher than Liza.

d.    If Liza took the same exam again she would earn the same score on the exam or lower 85% of the time.

11. A histogram that displays grouped data in which every class has the same frequency is described as a:

a.    Normal distribution

b.    Uniform distribution

c.    Bimodal distribution

d.   Skewed right distribution

12. If a set of data follows a normal distribution, and the mean is 70 with a standard deviation of 10, then approximately 99.7% of the data lies in a region centered around the mean between the     values of:

a.    60 and 80

b.    50 and 90

c.    40 and 100

d.    30 and 110

e.    20 and 120

13. For the set of data 8, 9, 10, 13, 13, 17, which statement is true?

a.    The mean is less than the median.

b.   The mean is equal to the median.

c.    The mean is less than the mode.

d.   The median is more than the mode.

e.    None of the above.

14. A sample of college students was asked to report the number of hours devoted to study during a typical week.  The histogram of the results is shown below.

Which of the following best describes the shape of the histogram?

a.    Skewed left

b.    Uniform

c.    Skewed right

d.    Bimodal

e.    Normal

15. The standard deviation of a sample of 64 observations equals 25. The variance of the sample equals

a.    5

b.   8

c.    625

d.   4,096

e.    None of the above.

Review for Chapters 5 and 6

16. Which of the following statements is true about a discrete probability distribution?

a.    The probability of each of the possible values of a random variable is included.

b.    Each individual probability must be between the values of 0 and 1, inclusive.

c.    The sum of all individual probabilities must be 1 or 100%.

d.   All of the above.

17. Let x represent the number of successes out of 10 trials in a binomial experiment. Which of the following expressions represents the statement, “The number of successes is at least 8”?

a. x ≤ 8

b. x < 8

c. x ≥ 8

d. x > 8

18. When asked, 70% of men polled will tell you they don’t like going to the doctor. Assuming we    randomly choose a group of 8 men, what is the probability at most 5 will report they do not like going to the doctor?

a.    0.194

b.   0.254

c.    0.448

d.   0.552

19. Seventy-six percent of sunflower seeds will germinate into a flower, and a sample of 800 such           sunflower seeds is randomly selected. The mean for the number of sunflower seeds in such samples of size 800 is _______.

a.    800

b.    608

c.    192

d.    247

20. Seventy-six percent of sunflower seeds will germinate into a flower, and a sample of 800 such          sunflower seeds is randomly selected. The standard deviation for the number of sunflower seeds in such samples of size 800 is _______.

a.    145.92

b.    24.66

c.    12.08

d.   0.18

21. The mean score on a standardized exam was 74 with a standard deviation of 8.3 .  A random sample of 35 students was selected, and their mean score on that exam was calculated. This mean belongs to a sampling distribution.  What is the mean of this sampling distribution?

a.    74

b.   8.3

c.    1.4

d.   0.24

22. The mean score on a standardized exam was 74 with a standard deviation of 8.3.  A random sample of 35 students was selected, and their mean score on that exam was calculated. This mean belongs to a sampling distribution.  What is the standard deviation for this sampling distribution?

a.    74

b.   8.3

c.    1.4

d.   0.24

23. For the standard normal distribution, what is ( < −1.23)?

a.    0.8906

b.   0.1151

c.    0.1093

d.   0.8849

24. Which of the following most closely defines the Central Limit Theorem?

a.    All sampling distributions are approximately normal, regardless of sample size.

b.   As long as the sample size is sufficiently large, the sampling distribution of the sample mean is approximately normal, regardless of the distribution of the population.

c.    All sampling distributions are approximately normal if the population is large enough.

d.   The sampling distribution of the sample mean looks more like the population distribution as the sample size increases.

25. Which of the following is NOT TRUE about the standard normal distribution?

a.    It is symmetric with a mean of 0 and a standard deviation of 1.

b.   Approximately 99.7% of its area exists from 3.00 standard deviations below the mean to 3.00 standard deviations above the mean.

c.    The proportion of area to the right of every z score is the same as the proportion of area to its left.

d.   The total area under its curve is equal to 1.

26. For the standard normal distribution, what is ( > −0.83)?

a.    0.7967

b.   0.2033

c.    0.8289

d.   0.1711

27. For the standard normal distribution, what is (0. 12 < < 1.47)?

a.    0.0885

b.   0.3814

c.    0.4770

d.   0.9115

28. For the standard normal distribution, what is the z score associated with the 40th  percentile?

a. z = 0.3446

b. z = 0.6554

c. z =   0.25

d. z = 0.25

29. For the standard normal distribution, find the z score which is the minimum for the top 10%.

a. z = 1.28

b. z = 1.28

c. z = 0.5398

d. z = 0.5398

30. The length of a fish in Keuka Lake is normally distributed with a mean of 12 inches and a standard   deviation of 1.5 inches.  Which graph below may represent the proportion of fish that are between

11 and 15 inches long?

.

12

.

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12

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Review for Chapters 7 and 8

31. Sandra usually jogs two miles per day. Based on 40 two-mile-jogs, she computed a 95 percent confidence interval for her mean jogging time (in minutes) to be (15.23, 15.97). Which of the  following statements is true with respect to the confidence level used?

a.    Sandra is 95 percent confident that the interval from 15.23 to 15.97 minutes contains the sample mean.

b.   Sandra is 95 percent confident that the interval from 15.23 to 15.97 minutes contains the population mean.

c.    There is a 95 percent chance that the mean time for another sample of 40 two-mile-jogs by Sandra will be between 15.23 and 15.97 minutes.

d.    Ninety-five percent of the sample jog times are between 15.23 and 15.97 minutes.

e.    Ninety-five percent of the time, Sandra’s time to run two miles will be between 15.23 and 15.97 minutes.

32. A random sample of 16 students selected from the student body of a large university had a mean age of 25 years and a standard deviation of 2 years.  A hypothesis test is done to determine if the mean    age of all the students at the university is significantly different from the claimed population mean     age of 24 years.  Assuming the distribution of the population of student ages is normal, the value of   the test statistic is:

a.    1.96

b.    2.00

c.    1.65

d.   0.50

e.    None of the above.

33. The state highway patrol conducted an analysis involving speeds of cars and their stopping                distances. A confidence interval needs to be constructed for the mean stopping distance of all cars  traveling at a particular speed. The state trooper conducting this analysis is considering using either a 90 percent confidence interval or a 95 percent confidence interval. Which of the following              statements about the length of these intervals is true?

a.    The 95 percent confidence interval will be longer than the 90 percent confidence interval.

b.   The 95 percent confidence interval will be shorter than the 90 percent confidence interval.

c.    Both intervals will be the same length, since they will be computed from the same sample.

d.   The length of each confidence interval will depend on the sample size, not on the confidence level.

e.   The length of each confidence interval will depend on the sample standard deviation, not on the confidence level.

34.  Forty randomly selected MTH 160 students at MCC are surveyed about their age in order to        estimate the mean age for all MTH 160 students at MCC.  Given the following Minitab output for the 40 ages, which of the following statements is true with respect to the confidence level used?

One-Sample T: Age

N Mean StDev SE Mean 98% CI for μ

40 22.075    4.994         0.790    (20.159, 23.991)

μ: mean of Age

a.    There is a 98 percent chance that the mean age for another sample of students will be between 20.159 and 23.991 years.

b.   The researcher is 98 percent confident that the interval from 20.159 to 23.991 years contains the sample mean.

c.    Ninety-eight percent of the sample’s ages are between 20.159 and 23.991 years.

d.    Ninety-eight percent of the time, the ages will be between 20.159 and 23.991 years.

e.   The researcher is 98 percent confident that the interval from 20.159 to 23.991 years contains the population mean.

35. Which of the following statements is true regarding the use of the Student t distribution for hypothesis testing of a population mean based on random samples of size n?

a.    The Student t distribution can be used for any n if the population has a distribution that is reasonably symmetrical and mound-shaped.

b.   The Student t distribution can only be used if the population standard deviation is known.

c.    The Student t distribution can only be used if n is greater than 30.

d.   When the Student t distribution is used, the number of degrees of freedom equals n.

e.    When the Student t distribution is used, n – 1 must be greater than 30.

36. When performing a hypothesis test, the decision is always made about

a.    The null hypothesis

b.   The alternative hypothesis

c.    Type I error

d.   The critical region

37. Five hundred members of a health club with a total of 10,000 members are selected at random and asked if they are satisfied or unsatisfied with the club’s facilities. Out of the 500 selected, 375 said  they were satisfied. Compute the point estimate for the probability that any of the 10,000                members selected at random will answer that they are satisfied with the club’s facilities.

a.    0.0375

b.   0.0875

c.    0.25

d.   0.75

38. A team of eye surgeons has developed a new technique for a risky eye operation to restore the     sight of people blinded from a certain disease. With the new technique, surgeons expect to           increase the number of patients who recover their eyesight to more than the 30% who recovered their eyesight with the old method. They decided to test the hypothesis p = 0.30 versus p > 0.30   where p is the proportion of successful operations (that for which the patients recovered their      sight). If 200 operations in various hospitals using the new method resulted in 74 that were           successful, which of the following is the test statistic for this test?

0.30 0.37

0.37 0.30

0.30 0.37

0.37 0.30

(0.30) (0.63)

200

0.37 0.30

(0.37) (0.63)

200

39. What is a Type II error?

a.    Rejecting a false null hypothesis.

b.    Rejecting a true null hypothesis.

c.    Failing to reject a true null hypothesis.

d.    Failing to reject a false null hypothesis.

40. A random sample of 100 shoppers at a clothing store was selected to estimate the proportion of  customers satisfied with the window displays. Let p represent the proportion of all shoppers who are satisfied with the window displays. What is the margin of error in estimating p if a 90 percent confidence interval is to be constructed? Assume a point estimate of pˆ 0.50 .

a.    0.003

b.   0.082

c.    0.098

d.   0.116

e.    0.139

41. The criteria for rejection of a null hypothesis in a P-value test is

a.    the P-value is less than the significance level .

b.   the P-value is less than or equal to the significance level .

c.    the P-value is equal to the significance level .

d.   the P-value is greater than or equal to the significance level .

e.   the P-value is greater than the significance level .

42. For which of the following hypothesis tests would the null hypothesis be rejected?

I.   Right-tail test; test statistic z = 2.03; significance level = 0.01

II.  Left-tail test; test statistic z = 2.03; significance level = 0.02

III. Two-tail test; test statistic z = 2.03; significance level = 0.05

a.    I only

b.    II only

c.    III only

d.    I, II, and III

e.    none of the

above

43. A Fair Isaac Corporation (FICO) score is used by credit agencies to assess the creditworthiness of      individuals. Its value ranges from 300 to 850. An individual with a FICO score over 700 is considered to be a quality credit risk. According to Fair Isaac Corporation, the mean FICO score is 703.5. A          credit analyst wondered whether high-income individuals had higher credit scores. Using a random sample of 40 high-income individuals, a test was conducted at the 0.05 level of significance. Choose the appropriate conclusion to this test.

N    Mean    StDev    SE Mean

40    714.2       83.2         13.16

μ: mean of Time

Test

Null hypothesis H₀: μ = 703.5

Alternative hypothesis H₁: μ > 703.5

T-Value    P-Value

0.81          0.21

a.    Since the P-value is greater than the level of significance, we reject the null hypothesis and   we have enough evidence to conclude that high-income individuals had higher credit scores.

b.   Since level of significance is smaller than the P-value, we reject the null hypothesis and we have enough evidence to conclude that high-income individuals had higher credit scores.

c.    Since the P-value is greater than the level of significance, the test is inconclusive.

d.   Since the P-value is greater than the level of significance, we fail to reject the null hypothesis and we do not have enough evidence to conclude that high-income individuals had higher     credit scores.

e.    Since the P-value is greater than the level of significance, we reject the alternative hypothesis and we have enough evidence to conclude that the mean FICO score is 703.5.

Review for Chapter 10

44. Which of the following statements about linear correlation is true?

a.    We say there is a negative correlation between x and y if the y values tend to increase as the corresponding x values increase.

b.   We say there is a positive correlation between x and y if the y values tend to increase as the corresponding x values increase.

c.    We say there is a positive correlation between x and y if the y values tend to increase as the corresponding x values decrease.

d.   We say there is a positive correlation between x and y if there is no distinct pattern in the scatterplot.

45. Which of the following is NOT a property of the linear correlation coefficient r?

a.    The value of r is always between 1 and 1, inclusive.

b.   The value of r measures the strength of a linear relationship.

c.    The linear correlation coefficient is robust. That is, a single outlier will not affect the value of r.

d.    The value of r is not affected if the independent and dependent variables are interchanged.

46. Match each of the following graphs with its corresponding linear correlation coefficient.

A

C

=  0.89           __________

=  −0.53       __________

B

D

=  0.82           __________

=  −0.83       __________

47. Match each of the following graphs with its corresponding linear correlation coefficient.

A

C

=  0.47           __________

=  −0.82       __________

B

D

=  0. 15           __________

=  −0.93       __________