2024 – 1 Finish times to the nearest hour for 60 dogsled teams are

   

1. Finish times (to the nearest hour) for 60 dogsled teams are shown below. Use five classes. Categorize the basic distribution shape as uniform, mound-shaped symmetric, bimodal, skewed left, or skewed right.

The relative frequency histogram of the above data is given below.

  

A)

mound-shaped symmetric

 

B)

Skewed right 

 

C)

Bimodal 

 

D)

Uniform or rectangular

 

E)

None of these 

·  

2. The initial visual impact of a scatter diagram depends on the scales used on the x and y axes. Consider the following data. 

  

x 

1 

2 

3 

4 

5 

6 

 

y 

1 

4 

6 

3 

6 

7 

Make a scatter diagram using the same scale on both the x and y axes (i.e., make sure the unit lengths on the two axes are equal). Draw the straight line that best fits the data points. 

  

A)

D)

 

B)

C)

 

E)

None of these

·  

3) The relationship between two variables, x and y, is depicted graphically below. Based on the scatter plot, we can conclude the following about the value of the linear correlation coefficient r. 

a) r 1 b) r – 1 c) r .8 d) r –.8 e) r 0 

4) Which of the probability distributions, depicted graphically below by probability

histograms, could be best modeled by the normal probability distribution?

a) b) 

c) d) 

e) None of these

5) A 2002 Employment Policy Foundation Report concluded that women held 49% of management and professional jobs in 2000. In a recent random sample, it was found that 52 out of 100 such jobs were held by women. Circle the correct hypotheses for testing at an = .05 significance level if the current proportion of management and professional jobs held by women exceeds .49. 

a) Ho: p = ..49 Ha: p < .49 b) Ho: p = .49 Ha: p > .49

c) Ho: p = .52 Ha: p < .52 d) Ho: p = .52 Ha: p > .52

e) None of these

6. Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 8.1 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is less than 8.1 seconds. What would you use for the alternative hypothesis?

  

A)

H1 : m   <   8.1 seconds

 

B)

H1 : m > 8.1 seconds

 

C)

H1 : m £ 8.1 seconds

 

D)

H1 : m ³ 8.1 seconds

 

E)

None of these

7. Suppose the age distribution of the Canadian population and the age distribution of a random sample of 531 residents in the Indian community of Red Lake are shown below.

  

Observed Number

 

Age (years)

Percent of   Canadian Population

in Red Lake   Village

 

Under 5

8.9%

49

 

5 to 14

11.9%

41

 

15 to 64

67.8%

389

 

65 and older

11.4%

52

Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. What are the degrees of freedom?

  

A)

7

 

B)

3

 

C)

5

 

D)

4

 

E)

None of these

8.If the p-value approach to hypothesis testing is used, the decision is based on 

a) comparing the p-value to the critical value 

b) comparing the test statistic to the critical value

c) comparing the p-value to the significance level

d) comparing the test statistic to the significance level

e) None of these

   

·  

  

9. In a   random In a random sample of 88 professional actors, it was found that 20   were extroverts. Let p represent the proportion of all actors who are   extroverts. Find a point estimate for p. (Round to the nearest thousandths.)

  

A)

68

 

B)

0.227

 

C)

20

 

D)

0.114

 

E)

None of these

·  

10. Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site.

1273 1231 1173 1228 1191 1206 1194 1227 1261

Given that the margin of error is find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round to the nearest tenth.)

  

A)

1200.1 to 1240.8

 

B)

1195.2.3 to 1245.7

 

C)

1203.5 to 1237.4

 

D)

1200.2 to 1240.7

 

E)

None of these

·  

11.Given that a 95% confidence interval for a population mean is (4, 10), we can conclude:

a) We are 95% confident that the sample mean lies between 4 and 10.

b) We are 95% confident that the population mean is 4 or 10.

c) The probability that lies between 4 and 10 is 95%.

d) We are 95% confident that the population mean lies between 4 and 10.

e) None of these.

12. Constructing a confidence interval is a procedure by which we form an interval of plausible values for 

a) a population parameter based on the information collected from a sample

b)a  sample statistic based on the information collected from a sample

c) a population parameter based on the information collected from a population

d) a sample statistic based on the information collected from a population

e) None of these

   

13.The Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Assume there is a physician at the park clinic in Grand Canyon Village. Suppose the physician has recorded (for a 5-year period) the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon.

  

Upper Canyon: Number of injuries per Landing Point   Between

North Canyon and Phantom Ranch

 

4

5

3

3

5

6

7

10

5

3

5

  

Lower Canyon: Number of injuries per Landing Point   Between

Bright Angel and Lava Falls

 

9

3

3

0

7

8

4

12

5

0

3

11

4

3

The mean, median, and mode for Upper Canyon are 5.091, 5.0, and 5, respectively.

The mean, median, and mode for Lower Canyon are 5.214, 4.0, and 3, respectively.

Compare the mean, median, and mode found in Upper Canyon and Lower Canyon, respectively.

  

A)

Lower Canyon mean is smaller than Upper Canyon, Lower   Canyon median is smaller than Upper Canyon, and Lower Canyon mode is smaller   than Upper Canyon.

 

B)

Lower Canyon mean is greater than Upper Canyon, Lower   Canyon median is greater than Upper Canyon, and Lower Canyon mode is smaller   than Upper Canyon.

 

C)

Lower Canyon mean is greater than Upper Canyon, Lower   Canyon median is smaller than Upper Canyon, and Lower Canyon mode is greater   than Upper Canyon.

 

D)

Lower Canyon mean is greater than Upper Canyon, Lower   Canyon median is smaller than Upper Canyon, and Lower Canyon mode is smaller   than Upper Canyon.

 

E)

None of these.

14. A data set consists of the following numbers: 1, 20, – 4, –20, 3, 10. The range of this dataset is 

a) 40 b) –9 c) 9 d) – 40 e) none of these 

15. The temperatures (in Fahrenheit) observed during seven days of summer in Los Angeles are 

78o, 99o, 68o, 91o, 99o, 75o, 78o

The median temperature for this sample of seven days is:

a) 91o  b) 89o c) 83.5o d) 78o 

e) none of these

16. Find the sample variance for the following sample data. Round your answer to the nearest hundredth.

  

24

16

13

31

28

  

A)

47.44

 

B)

78.80

 

C)

98.50

 

D)

59.30

 

E)

None of these

17. Richard has been given an 11-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. What is considered the success?

  

A)

number of questions

 

B)

Richard answers a question correctly.

 

C)

number of questions answered

 

D)

Richard is unable to answer a question correctly.

 

E)

None of these

18. Richard has been given a 5-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. Assuming that Richard guesses on all 5 questions in this binomial experiment, find the number of questions he can expect to answer correctly.

  

A)

All five questions.

 

B)

No questions.

 

C)

Three questions.

 

D)

Between one and two questions.

 

E)

None of these

19. Richard has been given a 12-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all 12 questions, what probabilities need to be added to determine the probability that he will answer no more than 3 questions correctly? 

  

A)

P(x=3)

 

B)

P(x=3)+P(x=4)+P(x=5)+P(x=6)+P(x=7)+P(x=8)+P(x=9)+P(x=10)+P(x=11)+P(x=12)

 

C)

P(x=0)+P(x=1)+P(x=2)+P(x=3)

 

D)

P(x=1)+P(x=2)

 

E)

None of these

20. The probability of a radar station detecting an enemy plane is 0.85. If 60 stations are in use, what is the probability of not detecting an enemy plane?

  

A)

0.15

 

B)

0.85

 

C)

0

 

D)

1

 

E)

None of these 

  

21. 

The annual incomes of all   MBA degree holders working in Los Angeles are approximately normally   distributed with a mean of $72,000 and a standard deviation of $12,000.   According to the empirical rule, the percentage of these MBA degree holders   with an annual income between $60,000 and $84,000 is approximately:

a)   50% b) 68% c) 95% d) 99.7% e) None of these

22. Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean m = 21.1 kilograms and standard deviation s = 3.7 kilograms. Let x be the weight of a fawn in kilograms. Convert the following z interval to a x interval. (Choose the closest value.)

–3.1 < z

  

A)

x < –9.63

 

B)

x < 9.63 

 

C)

x > 9.63

 

D)

x > 32.57

 

E)

None of these

23. Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities. (Round to the nearest thousandths.)

P(1 £ x £ 18); m = 12; s = 4

  

A)

0.997

 

B)

0.067

 

C)

0.106

 

D)

0.930

 

E)

None of these

  

24. 

The total area under a   symmetric continuous probability distribution curve, to the right of the mean   , is 

a)   1 b) 0 c) .5000 d) .2500 e) None of these

  

25. Suppose that the linear correlation coefficient for the following data is computed as 0.92

  

x

0.251

0.259

0.29

0.265

0.269

 

y

1.3

3.7

5.8

3.9

3.7

What can be concluded?

  

A)

There is evidence of a strong positive linear   correlation.

 

B)

There is no evidence of linear correlation.

 

C)

Changes in “x” cause changes in “y”.

 

D)

The appropriate function to model the data is an   exponential function.

 

E)

none of these 

26. It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:

  

x

5.00

5.75

6.50

7.25

8.25

 

y

40

40

67

71

98

Find b for the equation of the least-squares line given that , and .

  

A)

184.464

 

B)

18.51

 

C)

–443.493

 

D)

–58.064

 

E)

None of these

27. It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: (Round to the nearest tenth.)

  

x

5.25

5.75

6.50

7.00

7.75

 

y

38

37

66

80

82

Given that the equation of the regression line is at an archaeological site with elevation 7.5 (thousand feet), what does the least-squares equation predict for the percentage of culturally unidentified artifacts?

  

A)

82.6%

 

B)

87.9%

 

C)

17.4%

 

D)

12.1%

 

E)

None of these

28. Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? Let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximum wind speed (in miles per hour) of the cyclone. Suppose a random sample of cyclones gave the following information.

  

x

1014

935

980

955

995

 

y

50

80

60

135

84

Given that the value of r is –0.556, should y increase as x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Without performing a test for significance of r, would we be inclined, based on the value of r, to determine the regression line? Explain.

  

A)

Since r is zero, as x increases, y   remains the same. Yes, this is strongly correlated and we would determine the   regression line.

 

B)

Since r is negative, as x increases, y   decreases. The correlation coefficient does not indicate that we should   determine the regression line.

 

C)

Since r is negative, as x increases, y   increases. The correlation coefficient does not indicate we should determine   the regression line.

 

D)

Since r is positive, as x increases, y   increases. Yes, this is strongly correlated and we would determine the   regression line.

 

E)

None of these.

PART II: TRUE-FALSE 

29.  t tests of hypotheses are not dependent on the number of degrees of freedom.

30. The linear regression cannot be assumed to hold for values of the explanatory data far outside the range of that data.

31. The number of degrees of freedom in a chi-square goodness of fit test is the number of cells minus one.

32. The weights of kittens in a litter is a discrete variable.

33. The number of horses on a ranch is an example of a continuous variable.

34. The z-distribution is used to calculate the margin of error for an interval estimate of the mean if the population standard deviation is not known.

35. A Type I error occurs when a false null hypothesis is rejected.

36. A sampling distribution is a probability distribution for a parameter.

37. Let A be an event associated with sample space S. Let 

Ac be the complement of A, then A and Ac mutually exclusive.

38. Two events in a sample space A and B are dependent if knowing A occurs changes the probability that B will occur.

39. A point estimate is the value of a parameter that estimates the value of a statistic.

40. The mean of the standard normal distribution is one.