Statistics Final Review

Dr. Heather Gamber Name:

STATISTICS

FINAL REVIEW

Solve the problem.

1) Which of the following is not true of statistics?

A) Statistics collects and summarizes data.

B) Statistics allows conclusion about the data to be drawn.

C) Statistics answers questions with 100% certainty.

D) Statistics organizes and analyzes information.

2) A survey of 1544 American households found that 98% of the households own a computer. Identify the

population, the sample, and the individuals in the study.

3) Classify the colors of automobiles on a used car lot as qualitative data or quantitative data.

A) qualitative data B) quantitative data

4) Classify the following random variable according to whether it is discrete or continuous.

The number of cups of coffee sold in a cafeteria during lunch

A) discrete B) continuous

5) What method of data collection would you use to collect data for a study where a drug was given to 77 patients

and a placebo to another group of 77 patients to determine if the drug has an effect on a patient's illness?

A) observational study B) designed experiment

6) The government of a town needs to determine if the city's residents will support the construction of a new town

hall. The government decides to conduct a survey of a sample of the city's residents. Which one of the following

procedures would be most appropriate for obtaining a sample of the town's residents?

A) Survey a random sample of persons within each geographic region of the city.

B) Survey every 13th person who walks into city hall on a given day.

C) Survey the first 400 people listed in the town's telephone directory.

D) Survey a random sample of employees at the old city hall.

7) Every fifth teenager entering a concert is checked for possession of drugs. What sampling technique is used?

A) convenience B) stratified C) random D) systematic E) cluster

8) A local newspaper ran a survey by asking, "Do you support the deployment of a weapon that could kill millions

of innocent people?" Determine whether the survey design or the sampling method is biased.

9) The variable measured in the experiment is called ____________ .

A) a sampling unit B) the treatment

C) the response variable D) the predictor variable

1

10) Scott Tarnowski owns a pet grooming shop. His prices for grooming dogs are based on the size of the dog. His

records from last year are summarized below.

Class Frequency

Large 345

Medium 830

Small 645

Construct a frequency table including relative frequencies and percentages.

The bar graph shows the number of tickets sold each week by the garden club for their annual flower show.

11) During which week was the most number of tickets sold?

A) Week 4 B) Week 2 C) Week 5 D) Week 1

Solve the problem.

12) For the data below, construct a frequency polygon.

Height (in inches) Frequency

50 - 52 5

53 - 55 8

56 - 58 12

59 - 61 13

62 - 64 11

2

13) The grade point averages for 40 students are listed below. Construct a frequency distribution, a relative

frequency distribution, a cumulative frequency distribution, and a relative cumulative frequency distribution

using eight classes.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

3.1 2.4 2.4 2.3 1.6 1.6 4.0 3.1 3.2 1.8

2.2 2.2 1.7 0.5 3.6 3.4 1.9 2.0 3.0 1.1

3.0 4.0 4.0 2.1 1.9 1.1 0.5 3.2 3.0 2.2

14) The grade point averages for 40 students are listed below. Construct a frequency ogive using eight classes.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

3.1 2.4 2.4 2.3 1.6 1.6 4.0 3.1 3.2 1.8

2.2 2.2 1.7 0.5 3.6 3.4 1.9 2.0 3.0 1.1

3.0 4.0 4.0 2.1 1.9 1.1 0.5 3.2 3.0 2.2

15) The data below represent the consumption of coffee (in gallons) by adult Americans over a nine-year period.

Use a time series chart to display the data. Comment on the trend.

Year 1985 1986 1987 1988 1989 1990 1991 1992 1993

Coffee Consumption 10 11 11 12 13 14 15 15 13

16) A safety engineer wishes to use the following data to show the number of deaths from the collision of passenger

cars with trucks on a particular highway. Use a time series chart to display the data. Comment on the trend.

Year Number of Deaths

1930 12

1940 17

1950 22

1960 21

1970 16

1980 13

1990 11

17) Women were allowed to enter the Boston Marathon for the first time in 1972. Listed below are the winning

women's times (in minutes) for the first 10 years. Use a time series chart to display the data. Comment on the

trend.

Year

Time

1972 1973 1974 1975 1976 1977 1978 1979 1980 1981

190 186 167 162 167 168 165 155 154 147

3

Explain what is misleading about the graphic.

18)

The volume of our sales has doubled!!!

A) The length of a side has doubled, but the area has been multiplied by 8.

B) The length of a side has doubled, but the area has been unchanged.

C) The length of a side has doubled, but the area has been multiplied by 4.

D) The graphic is not misleading.

Solve the problem.

19) Describe the shape of the histogram. The data set: Pick Three Lottery

3 6 7 6 0 6 1 7 8 4

1 5 7 5 9 1 5 3 9 9

2 2 3 0 8 8 4 0 2 4

A) skewed to the left B) skewed to the right

C) symmetric D) uniform

20) Find the mean, median, and mode of the following numbers:

90 93 86 90 83 91 90 84 85 88

Find the range for the group of data items.

21) 9, 10, 11, 12, 13

A) 13 B) 11 C) 4 D) 9

Solve the problem.

22) Find the z-score for the value 61, when the mean is 68 and the standard deviation is 7.

A) z = -1.14 B) z = -1.00 C) z = -0.79 D) z = 0.79

23) The test scores of 30 students are listed below. Find the 30th percentile.

31 41 45 48 52 55 56 56 63 65

67 67 69 70 70 74 75 78 79 79

80 81 83 85 85 87 90 92 95 99

A) 67 B) 63 C) 56 D) 90

24) The test scores of 30 students are listed below. Find Q3.

31 41 45 48 52 55 56 56 63 65

67 67 69 70 70 74 75 78 79 79

80 81 83 85 85 87 90 92 95 99

A) 78 B) 31 C) 83 D) 85

4

25) To study the physical fitness of a sample of 28 people, the data below was collected representing the number of

sit-ups that a person could do in one minute.

10 12 12 15 15 15 18

20 22 25 25 26 29 30

32 33 40 40 40 45 46

47 48 48 50 52 53 56

Determine the lower and upper fences. Are there any outliers according to this criterion?

26) The selling prices of mutual funds change daily. In order to study these changes, a sample of mutual funds was

examined and the daily changes in price are listed below.

0.05, 0.00, -0.03, -0.01, 0.18, 0.00, 0.02, 0.29, 0.00, -0.07, 0.10, 0.07, 0.03

Determine the lower and upper fences. Are there any outliers according to this criterion?

27) A group of 79 students were asked how far they commute to work from home each time they go to work from

home. The results are given below. Would a drive of 15 miles be considered an outlier? Answer Yes or No.

Miles

traveled

Frequency

1 1

2 2

3 12

4 18

5 7

6 10

7 10

8 11

9 5

10 3

A) Yes B) No

28) A sample of 158-cell phone users were asked how many calls per day they received on their cell phones. The

results are given below. If a cell phone user only received 2 calls would that be considered an outlier? Answer

Yes or No.

Calls

Received

Frequency

8 - 11 18

12 - 15 23

16 - 19 38

20 - 23 47

24 - 27 32

A) No B) Yes

Use the scatter diagrams shown, labelled a through f to solve the problem.

5

29)

a

x1 2 3 4 5 6

y

12

10

8

6

4

2

x1 2 3 4 5 6

y

12

10

8

6

4

2

b

x1 2 3 4 5 6

y

12

10

8

6

4

2

x1 2 3 4 5 6

y

12

10

8

6

4

2

c

x1 2 3 4 5 6

y

12

10

8

6

4

2

x1 2 3 4 5 6

y

12

10

8

6

4

2

d

x1 2 3 4 5 6 7

y

12

10

8

6

4

2

x1 2 3 4 5 6 7

y

12

10

8

6

4

2

e

x1 2 3 4 5 6 7

y

12

10

8

6

4

2

x1 2 3 4 5 6 7

y

12

10

8

6

4

2

f

x1 2 3 4 5 6

y

12

10

8

6

4

2

x1 2 3 4 5 6

y

12

10

8

6

4

2

In which scatter diagram is r = 0.01?

A) e B) d C) f D) c

6

Solve the problem.

30) A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a

section of the county called East Meadow. One of the many variables thought to be an important predictor of

appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple

linear regression model:

y^ = β0 + β1x,

where y = appraised value of the house (in $thousands) and x = number of rooms. Using data collected for a

sample of n = 74 houses in East Meadow, the following results were obtained:

y^ = 74.80 + 22.86x

sβ = 71.24, t = 1.05 (for testing β0)

sβ = 2.63, t = 7.49 (for testing β1)

SSE = 60,775, MSE = 841, s = 29, r2 = .44

Range of the x-values: 5 - 11

Range of the y-values: 160 - 300

Give a practical interpretation of the estimate of the slope of the least squares line.

A) For each additional dollar of appraised value, we estimate the number of rooms in the house to increase

by 22.86 rooms.

B) For each additional room in the house, we estimate the appraised value to increase $74,800.

C) For a house with 0 rooms, we estimate the appraised value to be $74,800.

D) For each additional room in the house, we estimate the appraised value to increase $22,860.

31) The table below represents a random sample of the number of deaths per 100 cases for a certain illness over

time. If a person infected with this illness is randomly selected from all infected people, find the probability that

the person lives 3-4 years after diagnosis.

Years after Diagnosis Number deaths

1-2 15

3-4 35

5-6 16

7-8 9

9-10 6

11-12 4

13-14 2

15+ 13

A)35

65; 0.538 B)

1

35; 0.029 C)

35

100; 0.35 D)

7

120; 0.058

32) Which of the following cannot be a probability?

A)6

3B) -28 C) 0 D) 0.001

7

33) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on

any one of the five numbered spaces. If the pointer lands on a borderline, spin again.

Find the probability that the arrow will land on 1 or 2.

A)2

5B) 3 C)

2

3D) 1

34) The events A and B are mutually exclusive. If P(A) = 0.5 and P(B) = 0.1, what is P(A or B)?

A) 0.6 B) 0.4 C) 0.05 D) 0

35) Find the equation of the regression line for the given data.

x

y

-5

-10

-3

-8

4

9

1

1

-1

-2

-2

-6

0

-1

2

3

3

6

-4

-8

A) y^ = 2.097x + 0.552 B) y

^ = -0.552x + 2.097 C) y

^ = 2.097x - 0.552 D) y

^ = 0.522x - 2.097

36) Calculate the correlation coefficient, r, for the data below.

x

y

1

-1

3

1

10

18

7

10

5

7

4

3

6

8

8

12

9

15

2

1

A) 0.792 B) 0.990 C) 0.881 D) 0.819

37) The events A and B are mutually exclusive. If P(A) = 0.7 and P(B) = 0.2, what is P(A and B)?

A) 0.9 B) 0.14 C) 0.5 D) 0

38) You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 10.

A)1

13B)

9

10C)

12

13D)

1

10

39) Two events are __________________ if the occurrence if the occurrence of event E in a probability experiment

does not affect the probability of event F in the same experiment.

A) Dependent B) Independent

C) Mutually exclusive D) Disjoint

40) A single die is rolled twice. Find the probability of getting a 3 the first time and a 5 the second time.

A)1

3B)

1

12C)

1

36D)

1

6

8

41) A human gene carries a certain disease from the mother to the child with a probability rate of 35%. That is, there

is a 35% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has five

children. Assume that the infections of the five children are independent of one another. Find the probability

that at least one of the children get the disease from their mother.

A) 0.116 B) 0.884 C) 0.312 D) 0.062

42) Consider the discrete probability distribution to the right when answering the following question. Find the

probability that x equals 4.

x 3 4 7 8

P(x) 0.11 ? 0.18 0.3

A) 0.59 B) 1.64 C) 2.36 D) 0.41

43) The random variable x represents the number of boys in a family of three children. Assuming that boys and

girls are equally likely, (a) construct a probability distribution, and (b) graph the probability histogram.

44) Calculate the mean for the discrete probability distribution shown here.

X 3 5 8 11

P(X) 0.01 0.32 0.06 0.61

A) 8.82 B) 2.205 C) 27 D) 6.75

45) A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab

conducts. Prices for each weekly shipment of rats follow the distribution below:

Price $10.00 $12.50 $15.00

Probability 0.35 0.3 0.35

How much should the lab budget for next year's rat orders assuming this distribution does not change. (Hint:

find the expected price.)

A) $12.50 B) $650.00 C) $1250.00 D) $3,380,000.00

46) The random variable x represents the number of boys in a family of three children. Assuming that boys and

girls are equally likely, find the mean and standard deviation for the random variable x.

A) mean: 2.25; standard deviation: 0.87 B) mean: 2.25; standard deviation: 0.76

C) mean: 1.50; standard deviation: 0.87 D) mean: 1.50; standard deviation: 0.76

47) Decide whether the experiment is a binomial experiment. If it is not, explain why. You roll a die 50 times. The

random variable represents the number that appears on each roll of the die.

48) Assume that male and female births are equally likely and that the birth of any child does not affect the

probability of the gender of any other children. Find the probability of exactly nine boys in ten births.

A) 0.020 B) 0.9 C) 0.09 D) 0.010

49) Assume that male and female births are equally likely and that the birth of any child does not affect the

probability of the gender of any other children. Suppose that 600 couples each have a baby; find the mean and

standard deviation for the number of girls in the 600 babies.

9

50) Draw the probability histogram and label the mean for n = 6 and p = 0.4

51) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 68°F

to 88°F. What is the probability that a randomly selected August day has a high temperature that exceeded

73°F?

A) 0.4679 B) 0.05 C) 0.25 D) 0.75

52) The data below are the final exam scores of 10 randomly selected statistics students and the number of hours

they studied for the exam. Construct a scatter diagram for the data.

Hours, x

Scores, y

3

65

5

80

2

60

8

88

2

66

4

78

4

85

5

90

6

90

3

71

53) You are performing a study about the weight of preschoolers. A previous study found the weights to be

normally distributed with a mean of 30 and a standard deviation of 4. You randomly sample 30 preschool

children and find their weights to be as follows.

25 25 26 26.5 27 27 27.5 28 28 28.5

29 29 30 30 30.5 31 31 32 32.5 32.5

33 33 34 34.5 35 35 37 37 38 38

a) Draw a histogram to display the data. Is it reasonable to assume that the weights are normally distributed?

Why?

b) Find the mean and standard deviation of your sample.

c) Is there a high probability that the mean and standard deviation of your sample are consistent with those

found in previous studies? Explain your reasoning.

54) The graph of a normal curve is given. Use the graph to identify the value of μ and σ.

3 6 9 12 15 18 21

A) μ = 3, σ = 12 B) μ = 12, σ = 9 C) μ = 9, σ = 12 D) μ = 12, σ = 3

10

55) The analytic scores on a standardized aptitude test are known to be normally distributed with mean μ = 610 and

standard deviation σ = 115.

(a) Draw a normal curve with the parameters labeled.

(b) Shade the region that represents the proportion of test takers who scored less than 725.

(c) Suppose the area under the normal curve to the left of X = 725 is 0.8413. Provide two interpretations of this

result.

A random variable X is normally distributed with μ = 60. Convert the value of X to a Z-score, if the standard deviation is

as given.

56) X = 70; σ = 10

A) 10 B) 1 C) 6 D) 70

Solve the problem.

57) Find the area under the standard normal curve between z = 0 and z = 3.

A) 0.9987 B) 0.0010 C) 0.4641 D) 0.4987

58) IQ test scores are normally distributed with a mean of 105 and a standard deviation of 15. An individual's IQ

score is found to be 126. Find the z-score corresponding to this value.

A) -1.40 B) -0.71 C) 0.71 D) 1.40

59) For a standard normal curve, find the z-score that separates the bottom 90% from the top 10%.

A) 1.28 B) 2.81 C) 0.28 D) 1.52

Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the

percentage of buyers who paid:

60) more than $153,200 if the standard deviation is $1600.

A) 47.5% B) 97.5% C) 95% D) 2.5%

Solve the problem.

61) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this

event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a

standard deviation of 50 seconds. The fitness association wants to recognize the fastest 10% of the boys with

certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition

from the fitness association?

A) 532.25 seconds B) 514 seconds C) 367.75 seconds D) 386 seconds

62) Suppose that four students paid the following amounts for textbooks this semester:

$90, $110, $150, $190. Using a sample size of 3, find the mean and standard deviation of the sampling

distribution.

A) μx = 90; σx = 18.3 B) μx = 135; σx = 18.3

C) μx = 90; σx = 19.2 D) μx = 135; σx = 19.2

11

63) The number of violent crimes committed in a day possesses a distribution with a mean of 2.8 crimes per day and

a standard deviation of 4 crimes per day. A random sample of 100 days was observed, and the sample mean

number of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.

A) shape unknown with mean = 2.8 and standard deviation = 4

B) approximately normal with mean = 2.8 and standard deviation = 4

C) shape unknown with mean = 2.8 and standard deviation = 0.4

D) approximately normal with mean = 2.8 and standard deviation = 0.4

64) A farmer was interested in determining how many grasshoppers were in his field. He knows that the

distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he

drives his tractor down each row he counts how many grasshoppers he sees flying away. After 40 rows he

figures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of the

farmer will count 60 or more flights average in the next 40 rows down which he drives his tractor?

A) 0.0571 B) 0.5710 C) 0.4429 D) 0.9429

65) Professor Whata Guy too a survey of his Introduction To Statistics Class of 420 students. One of the questions

was "Will you take another mathematics class?" The results showed that 252 of the students said yes. What is

the sample proportion, p^?

A) 0.252 B) 0.775 C) 0.6 D) 0.42

66) Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that for

the afternoon shift 5% of all welds done will be substandard. If Smith checks 300 of the 7500 welds completed

that shift, what is the probability that he will find less than 20 substandard welds?

A) 0.0934 B) 0.9066 C) 0.4066 D) 0.5934

67) Private colleges and universities rely on money contributed by individuals and corporations for their operating

expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest

earned by the fund. A recent survey of eight private colleges in the United States revealed the following

endowments (in millions of dollars): 72.5, 59.3, 234.7, 483.8, 113.1, 185.3, 94.4, and 216.8. What value will be used

as the point estimate for the mean endowment of all private colleges in the United States?

A) 208.557 B) 8 C) 182.488 D) 1459.9

68) Compute the critical value zα/2 that corresponds to a 95% level of confidence.

A) 2.575 B) 1.96 C) 1.645 D) 2.33

69) A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight

is (1.1%, 3.4%). What is the point estimator of the mean percentage of reservations that are canceled on the day

of the flight?

A) 1.15% B) 1.70% C) 2.3% D) 2.25%

70) The standard IQ test has a mean of 97 and a standard deviation of 16. We want to be 95% certain that we are

within 4 IQ points of the true mean. Determine the required sample size.

A) 159 B) 1 C) 62 D) 8

12

71) Which of the following is not a characteristic of Students' t distribution?

A) symmetric distribution

B) mean of 1

C) depends on degrees of freedom.

D) For large samples, the t and z distributions are nearly equivalent.

72) Let t0 be a specific value of t. Find t0 such that the following statement is true:

P(t ≤ t0) = .005 where df = 20

A) 2.845 B) 2.861 C) -2.861 D) -2.845

73) How much money does the average professional football fan spend on food at a single football game? That

question was posed to 10 randomly selected football fans. The sampled results show that sample mean and

standard deviation were $15.00 and $3.20, respectively. Use this information to create a 98% confidence interval

for the mean.

A) 15 ± 2.764(3.20/ 10) B) 15 ± 2.262(3.20/ 10)

C) 15 ± 2.821(3.20/ 10) D) 15 ± 2.718(3.20/ 10)

74) The mean age of bus drivers in Chicago is 58.9 years. Write the null and alternative hypotheses.

75) The mean age of bus drivers in Chicago is 56.6 years. If a hypothesis test is performed, how should you interpret

a decision that rejects the null hypothesis?

A) There is sufficient evidence to support the claim μ = 56.6.

B) There is not sufficient evidence to support the claim μ = 56.6.

C) There is sufficient evidence to reject the claim μ = 56.6.

D) There is not sufficient evidence to reject the claim μ = 56.6.

76) The mean age of bus drivers in Chicago is 47.5 years. Identify the type I and type II errors for the hypothesis test

of this claim.

77) Find the critical value for a left-tailed test with α = 0.025.

A) -2.575 B) -2.24 C) -1.645 D) -1.96

78) You wish to test the claim that μ > 16 at a level of significance of α = 0.05 and are given sample statistics n = 50,

x = 16.3, and σ = 1.2. Compute the value of the test statistic. Round your answer to two decimal places.

A) 2.31 B) 3.11 C) 1.77 D) 0.98

79) Suppose you are using α = 0.05 to test the claim that μ > 12 using a P-value. You are given the sample statistics

n = 50, x = 12.3, and σ = 1.2. Find the P-value.

A) 0.0384 B) 0.0128 C) 0.1321 D) 0.0012

80) A random sample of 56 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31

hours. A leading consumer journal states that the mean life for these bulbs is μ = 639 hours. Test this hypothesis

by constructing a 95% confidence interval for the population mean.

13

81) True or False: Results that are statistically significant are always practically significant.

A) True B) False

82) Find the standardized test statistic t for a sample with n = 12, x = 17.2, s = 2.2, and α = 0.01 if H0: μ = 16. Round

your answer to three decimal places.

A) 1.991 B) 1.890 C) 2.001 D) 2.132

83) The business college computing center wants to determine the proportion of business students who have

personal computers (PC's) at home. If the proportion exceeds 25%, then the lab will scale back a proposed

enlargement of its facilities. Suppose 200 business students were randomly sampled and 65 have PC's at home.

Find the rejection region for this test using α = .01.

A) Reject H0 if z < -2.33. B) Reject H0 if z = 2.33.

C) Reject H0 if z > 2.33. D) Reject H0 if z > 2.575 or z < -2.575.

84) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 15% of

the women who actually have the disease. A new method has been developed that researchers hope will be able

to detect cancer more accurately. A random sample of 90 women known to have breast cancer were screened

using the new method. Of these, the new method failed to detect cancer in 10. Is the sample size sufficiently

large in order to conduct this test of hypothesis? Explain.

14

Answer KeyTestname: STATISTICS FINAL REVIEWF-06

1) C

2) population: collection of American households; sample: collection of 1544 American households surveyed; individuals:

each household

3) A

4) A

5) B

6) A

7) D

8) The wording of the question is biased, as it tends to encourage negative responses.

9) C

10) Class Frequency Relative Frequency Percentage

Large 345 .190 19.0

Medium 830 .456 45.6

Small 645 .354 35.4

Total 1820 1.000 100.0

11) A

12)

13)

GPA Frequency

Relative

Frequency

Cumulative

Frequency

Cumulative

Relative Frequency

0.5-0.9

1.0-1.4

1.5-1.9

2.0-2.4

2.5-2.9

3.0-3.4

3.5-3.9

4.0-4.4

4

2

7

9

2

10

2

4

0.10

0.05

0.175

0.225

0.05

0.25

0.05

0.10

4

6

13

22

24

34

36

40

0.10

0.15

0.325

0.55

0.60

0.85

0.90

1

15


14)

15)

In general, there is an increasing trend in the coffee consumption of adult Americans. However, beginning in 1993,

there is sign of a decreasing trend.

16


16)

From 1930 to 1950, there was an increasing trend in the number of collisions deaths. Subsequently, there was a

decreasing trend.

17)

In general, there was a decreasing trend in women's Boston marathon times.

18) C

19) D

20) mean 88, median 89, mode 90

21) C

22) B

23) B

24) C

25) lower fence = -24; upper fence = 88; outliers: none

26) lower fence = -0.13; upper fence = 0.19; outliers: 0.29

27) A

28) A

29) A

30) D

31) C

32) B

33) A

34) A

35) C

17


36) B

37) D

38) C

39) B

40) C

41) B

42) D

43) (a)

x P(x)

01

8

13

8

23

8

31

8

(b)

44) A

45) B

46) C

47) Not a binomial experiment. There are more than two outcomes.

48) D

49) μ = np = 600(0.5) = 300; σ = npq = 600(0.5)(0.5) = 12.25

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50)

51) D

52)

19


53) (a)

It is not reasonable to assume that the heights are normally distributed since the histogram is skewed.

(b) μ = 31, σ = 3.86

(c) Yes. The mean and standard deviation are close.

54) D

55) (a), (b)

(c) The two interpretations are: (1) the proportion of test takers who scored less than 725 is 0.8413 and (2) the

probability that a randomly selected test taker has a score less than 725 is 0.8413.

56) B

57) D

58) D

59) A

60) D

61) D

62) D

63) D

64) A

65) C

66) B

67) C

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68) B

69) D

70) C

71) B

72) D

73) C

74) H0: μ = 58.9, H1: μ ≠ 58.9

75) C

76) type I: rejecting H0: μ = 47.5 when μ = 47.5

type II: failing to reject H0: μ = 47.5 when μ ≠ 47.5

77) D

78) C

79) A

80) Since μ is in (636.9, 653.1), we do not reject H0.

81) B

82) B

83) C

84) To determine if the sample size is large enough for the test of hypothesis to work properly, we need to calculate the

interval p0 ± 3σp^.

p0 ± 3σp^ = p0 ± 3

p0q0

n = .15 ± 3

.15(.85)

90 = .15 ± 3(.038) ⇒ (.037, .263)

Since this interval does not include the values of 0 or 1, the sample size of n = 90 is large enough for the test of

hypothesis to work properly.

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Statistics Final Review