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# Collaborative Statistics: Practice Final Exam 1 (Modified R. Bloom)

Module by: Roberta Bloom. E-mail the author

Summary: This module is a practice final for an associated elementary statistics textbook, Collaborative Statistics. Some problems from the original module by S. Dean and B. Illowsky have been modified and some new problems have been added.

Questions 1-2 refer to the following:

An experiment consists of tossing one 6-sided die

• Let Event AA = the die shows an even number
• Let Event BB = the die shows a number greater than 4

## Exercise 1

Events AA and BB are:

• A. Mutually exclusive.
• B. Independent.
• C. Mutually exclusive and independent.
• D. Neither mutually exclusive nor independent.

### Solution

B: Independent, because P(A) = 3/6 = 1/2 and P(A|B) = 1/2

## Exercise 2

Suppose that the die is rolled twice, rather than once. Find the probability of rolling an even number on at least one die. Find P ( A on first toss or A on second toss ) P ( A on first toss or A on second toss )

• A. 1 4 1 4
• B. 2 4 2 4
• C. 3 4 3 4
• D. 2 3 2 3
• E. 1

C: 3 4 3 4

## Exercise 3

Which of the following are TRUE when we perform a hypothesis test on matched or paired samples?

• A. Sample sizes are almost never small.
• B. Two measurements are drawn from the same pair of individuals or objects.
• C. Two sample averages are compared to each other.
• D. Answer choices B and C are both true.

### Solution

B: Two measurements are drawn from the same pair of individuals or objects. (C is not correct because in a paired test we use the DIFFERENCES as the data and the test uses the average of the differences, rather than directly comparing the sample averages.)

Questions 4 - 5 refer to the following:

118 students were asked what type of color their bedrooms were painted: light colors, dark colors or vibrant colors. The results were tabulated according to gender.

Table 1
Light colors Dark colors Vibrant colors
Female 20 22 28
Male 10 30 8

## Exercise 4

Find the probability that a randomly chosen student is male or has a bedroom painted with light colors.

• A. 10 118 10 118
• B. 68 118 68 118
• C. 48 118 48 118
• D. 10 48 10 48

B: 68 118 68 118

## Exercise 5

Find the probability that a randomly chosen student is male given the student’s bedroom is painted with dark colors.

• A. 30 118 30 118
• B. 30 48 30 48
• C. 22 118 22 118
• D. 30 52 30 52

### Solution

D: 30 52 30 52

Questions 6 – 7 refer to the following:

We are interested in the number of times a teenager must be reminded to do his/her chores each week. A survey of 40 mothers was conducted. The table below shows the results of the survey.

 XX P ( x ) P ( x ) 0 2 40 2 40 1 5 40 5 40 2 3 14 40 14 40 4 7 40 7 40 5 4 40 4 40

## Exercise 6

Find the probability that a teenager is reminded 2 times.

• A. 8
• B. 8 40 8 40
• C. 6 40 6 40
• D. 2

B: 8 40 8 40

## Exercise 7

Find the expected number of times a teenager is reminded to do his/her chores.

• A. 15
• B. 2.78
• C. 1.0
• D. 3.13

### Solution

B: 2.78

Questions 8 – 9 refer to the following:

On any given day, approximately 37.5% of the cars parked in the De Anza parking structure are parked crookedly. (Survey done by Kathy Plum.) We randomly survey 22 cars. We are interested in the number of cars that are parked crookedly.

## Exercise 8

For every 22 cars, how many would you expect to be parked crookedly, on average?

• A. 8.25
• B. 11
• C. 18
• D. 7.5

A: 8.25

## Exercise 9

What is the probability that at least 10 of the 22 cars are parked crookedly.

• A. 0.1263
• B. 0.1607
• C. 0.2870
• D. 0.8393

C: 0.2870

## Exercise 10

Using a sample of 15 Stanford-Binet IQ scores, we wish to conduct a hypothesis test. Our claim is that the average IQ score on the Stanford-Binet IQ test is more than 100. It is known that the standard deviation of all Stanford-Binet IQ scores is 15 points. The correct distribution to use for the hypothesis test is:

• A. Binomial
• B. Student-t
• C. Normal
• D. Uniform
• E. Chi-Square

### Solution

C: Normal

Questions 11 – 13 refer to the following:

De Anza College keeps statistics on the pass rate of students who enroll in math classes. In a sample of 1795 students enrolled in Math 1A (1st quarter calculus), 1428 passed the course. In a sample of 856 students enrolled in Math 1B (2nd quarter calculus), 662 passed. In general, are the pass rates of Math 1A and Math 1B statistically the same? Let A = the subscript for Math 1A and B = the subscript for Math 1B.

## Exercise 11

If you were to conduct an appropriate hypothesis test, the alternate hypothesis would be:

• A. H a H a : p A p A = p B p B
• B. H a H a : p A p A > p B p B
• C. H o H o : p A p A = p B p B
• D. H a H a : p A p A p B p B

### Solution

D: H a H a : p A p A p B p B

## Exercise 12

The Type I error is to:

• A. believe that the pass rate for Math 1A is the same as the pass rate for Math 1B when, in fact, the pass rates are different.
• B. believe that the pass rate for Math 1A is different than the pass rate for Math 1B when, in fact, the pass rates are the same.
• C. believe that the pass rate for Math 1A is greater than the pass rate for Math 1B when, in fact, the pass rate for Math 1A is less than the pass rate for Math 1B.
• D. believe that the pass rate for Math 1A is the same as the pass rate for Math 1B when, in fact, they are the same.

### Solution

B: believe that the pass rate for Math 1A is different than the pass rate for Math 1B when, in fact, the pass rates are the same.

## Exercise 13

The correct decision is:

• A. Reject H o H o
• B. Do not reject H o H o
• C. Can not make a decision because of lack of information

### Solution

B: Do not reject H o H o

Kia, Alejandra, and Iris are runners on the track teams at three different schools. Their running times, in minutes, and the statistics for the track teams at their respective schools, for a one mile run, are given in the table below:

Table 3
Running Time School Average Running Time School Standard Deviation
Kia 4.9 5.2 .15
Alejandra 4.2 4.6 .25
Iris 4.5 4.9 .12

## Exercise 14

Which student is the BEST when compared to the other runners at her school?

• A. Kia
• B. Alejandra
• C. Iris
• D. Both Iris and Alejandra
• E. Impossible to determine

### Solution

C: Iris

Questions 15 – 17 refer to the following:

The following are a random sample of adult ski sweater prices are from the Gorsuch Ltd. Winter catalog:

{ $212 ,$292 ,$278 ,$199 $280 ,$236 } { $212 ,$292 ,$278 ,$199 $280 ,$236 }

Assume the underlying sweater price population is approximately normally distributed. A hypothesis test is done to determine whether the average price of all adult ski sweaters from Gorsuch Ltd. is at least $275. ## Exercise 15 The correct distribution to use for the hypothesis test is: • A. Normal • B. Binomial • C. Student-t • D. Exponential ### Solution C: Student-t ## Exercise 16 The hypothesis test: • A. is two-tailed • B. is left-tailed • C. is right-tailed • D. has no tails ### Solution B: is left-tailed ## Exercise 17 The correct conclusion for this test is • A. The true average price of all adult ski sweaters in this catalog is more than$275.
• B. The true average price of all adult ski sweaters in this catalog NOT more than $275. • C. The true average price of all adult ski sweaters in this catalog is less than$275.
• D. The true average price of all adult ski sweaters in this catalog is NOT less than $275. • D. The true average price of all adult ski sweaters in this catalog is$249.50

• D. The true average price of all adult ski sweaters in this catalog is NOT less than $275. ## Exercise 18 Sara, a statistics student, wanted to determine the average number of books that college professors have in their office. She randomly selected 2 buildings on campus and asked each professor in the selected buildings how many books are in his/her office. Sara surveyed 25 professors. The type of sampling selected is a: • A. simple random sampling • B. systematic sampling • C. cluster sampling • D. stratified sampling ### Solution C: cluster sampling ## Exercise 19 A clothing store would use which measure of the center of data when placing orders? • A. Mean • B. Median • C. Mode • D. IQR ### Solution C: Mode ## Exercise 20 In a hypothesis test, the p-value is • A. the probability that an outcome of the data will happen purely by chance when the null hypothesis is true. • B. called the preconceived alpha. • C. compared to beta to decide whether to reject or not reject the null hypothesis. • D. Answer choices A and B are both true. • E. Answer choices B and C are both true. ### Solution A: the probability that an outcome of the data will happen purely by chance when the null hypothesis is true. Questions 21 - 23 refer to the following: A community college offers classes 6 days a week: Monday through Saturday. Maria conducted a study of the students in her classes to determine how many days per week the students who are in her classes come to campus for classes. In each of her 5 classes she randomly selected 10 students and asked them how many days they come to campus for classes. The results of her survey are summarized in the table below. Table 4 Number of Days on Campus Frequency Relative Frequency Cumulative Relative Frequency 1 2 2 12 .24 3 10 .20 4 .98 5 0 6 1 .02 1.00 ## Exercise 21 Combined with convenience sampling, what other sampling technique did Maria use? • A. simple random • B. systematic • C. cluster • D. stratified ### Solution D: stratified ## Exercise 22 How many students come to campus for classes 4 days a week? • A. 49 • B. 25 • C. 30 • D. 13 • E. 24 ### Solution B: 25 ## Exercise 23 What is the 60th percentile for the this data? • A. 2 • B. 3 • C. 4 • D. 5 ### Solution C: 4 The next two questions refer to the following: The following data are the results of a random survey of 110 Reservists called to active duty to increase security at California airports. Table 5 Number of Dependents Frequency 0 11 1 27 2 33 3 20 4 19 ## Exercise 24 Construct a 95% Confidence Interval for the true population average number of dependents of Reservists called to active duty to increase security at California airports. • A. (1.85, 2.32) • B. (1.80, 2.36) • C. (1.97, 2.46) • D. (1.92, 2.50) ### Solution A: (1.85, 2.32) ## Exercise 25 The 95% confidence Interval above means: • A. 5% of Confidence Intervals constructed this way will not contain the true population aveage number of dependents. • B. We are 95% confident the true population average number of dependents falls in the interval. • C. Both of the above answer choices are correct. • D. None of the above. ### Solution C: Both above are correct. ## Exercise 26 X~X~ U ( 4 , 10 ) U ( 4 , 10 ) . Find the 30th percentile. • A. 0.3000 • B. 3 • C. 5.8 • D. 6.1 ### Solution C: 5.8 ## Exercise 27 If X~X~ Exp ( 0.8 ) Exp ( 0.8 ) , then P ( X<μ ) P ( X<μ ) = • A. 0.3679 • B. 0.4727 • C. 0.6321 • D. 0.5 • E. cannot be determined ### Solution C: 0.6321 ## Exercise 28 The lifetime of a computer circuit board is normally distributed with a mean of 2500 hours and a standard deviation of 60 hours. What is the probability that a randomly chosen board will last at most 2560 hours? • A. 0.8413 • B. 0.1587 • C. 0.3461 • D. 0.6539 ### Solution A: 0.8413 ## Exercise 29 A survey of 123 Reservists called to active duty as a result of the September 11, 2001, attacks was conducted to determine the proportion that were married. Eighty-six reported being married. Construct a 98% confidence interval for the true population proportion of reservists called to active duty that are married. • A. (0.6030, 0.7954) • B. (0.6181, 0.7802) • C. (0.5927, 0.8057) • D. (0.6312, 0.7672) ### Solution A: (0.6030, 0.7954) ## Exercise 30 Winning times in 26 mile marathons run by world class runners average 145 minutes with a standard deviation of 14 minutes. A sample of the last 10 marathon winning times is collected. Let x¯ x = average winning times for 10 marathons. The distribution for x¯ x is: • A. N 145 14 10 N 145 14 10 • B. N 145 14 N 145 14 • C. t 9 t 9 • D. t 10 t 10 ### Solution A: N 145 14 10 N 145 14 10 ## Exercise 31 Suppose that Phi Beta Kappa honors the top 1% of college and university seniors. Assume that grade point averages (G.P.A.) at a certain college are normally distributed with a 2.5 average and a standard deviation of 0.5. What would be the minimum G.P.A. needed to become a member of Phi Beta Kappa at that college? • A. 3.99 • B. 1.34 • C. 3.00 • D. 3.66 • E. 3.42 ### Solution D: 3.66 The number of people living on American farms has declined steadily during this century. Here are data on the farm population (in millions of persons) from 1935 to 1980. Table 6 Year 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 Population 32.1 30.5 24.4 23.0 19.1 15.6 12.4 9.7 8.9 7.2 The linear regression equation is y-hat = 1166.93 – 0.5868x ## Exercise 32 What was the expected farm population (in millions of persons) for 1980? • A. 7.2 • B. 5.1 • C. 6.0 • D. 8.0 ### Solution B: 5.1 ## Exercise 33 In linear regression, which of the following values for the SSE (sum of squared errors) is best? • A. 13.46 • B. 18.22 • C. 24.05 • D. 16.33 ### Solution A: 13.46 ## Exercise 34 In regression analysis, if the correlation coefficient is close to 1 what can be said about the best fit line? • A. It is a horizontal line. Therefore, we can not use it. • B. There is a strong linear pattern. Therefore, it is most likely a good model to be used. • C. The coefficient correlation is close to the limit. Therefore, it is hard to make a decision. • D. We do not have the equation. Therefore, we can not say anything about it. ### Solution B: There is a strong linear pattern. Therefore, it is most likely a good model to be used. Question 35-37 refer to the following: A study of the career plans of young women and men sent questionnaires to all 722 members of the senior class in the College of Business Administration at the University of Illinois. One question asked which major within the business program the student had chosen. Here are the data from the 386 students who responded. Table 7: Does the data suggest that there is a relationship between the gender of students and their choice of major? Female Male Accounting 68 56 Administration 91 40 Ecomonics 5 6 Finance 61 59 ## Exercise 35 The distribution for the test is: • A. Chi 2 8 Chi 2 8 • B. Chi 2 3 Chi 2 3 • C. t 722 t 722 • D. N ( 0 ,1 ) N ( 0 ,1 ) • E. t 7 t 7 ### Solution B: Chi 2 3 Chi 2 3 ## Exercise 36 The expected number of female who choose Finance is : • A. 37 • B. 61 • C. 60 • D. 70 ### Solution D: 70 ## Exercise 37 The p-value is 0.0127. The conclusion to the test is: • A. The choice of major and the gender of the student are independent of each other. • B. The choice of major and the gender of the student are not independent of each other. • C. The choice of major and gender are not uniformly distributed. • D. More females prefer Administration than males. ### Solution B: The choice of major and the gender of the student are not independent of each other. ## Questions 38 thorugh 39 refer to the following An agency reported that the work force nationwide is composed of 10% professional, 10% clerical, 30% skilled, 15% service, and 35% semiskilled laborers. A random sample of 100 San Jose residents indicated 15 professional, 15 clerical, 40 skilled, 10 service, and 20 semiskilled laborers. At αα = .10 does the work force in San Jose appear to be consistent with the agency report for the nation? ## Exercise 38 Which kind of hypothesis test is appropriate? • A. Chi 2 Chi 2 goodness of fit • B. Chi 2 Chi 2 test of independence • C. Independent groups proportions • D. Unable to determine ### Solution A: Chi 2 Chi 2 goodness of fit ## Exercise 39 Find the p-value. • A. 0.0025 • B. 0.9975 • C. 0.0057 • D. 1.0 • E. None of these is correct ### Solution A. 0.0025 ## Exercise 40 Cindy buys tickets from a raffle that has 2000 tickets. There is 1 grand prize of$15000 and there are 5 more prizes of $500 each. A ticket costs$10. Find the expected value of a raffle ticket.

• A. $8.75 profit • B.$2.31 loss
• C. $8.72 gain • D.$1.22 loss

## Exercise 41

According to a 2009 Gallup-Healthways Well-Being poll, 16 percent of American adults lack (do not have) health insurance. Suppose a study is being done to investigate the reasons why people do not have health insurance. Find the probability that at least 4 American adults must be interviewed in order to find one that lacks health insurance.

• A. 0.407
• B. 0.003
• C. 0.593
• D. 0.25
• E. Not enough information given to answer this question

C. 0.593

## Exercise 42

Suppose that the time that it takes to repair a furnace at Ace Furnace Repair is uniformly distributed between 1.5 and 4 hours. Find the probability that the average repair time for a random sample of 36 furnace repairs is less than 3 hours.

• A. 0.6
• B. 0.0.667
• C. 0.635
• D. 0.923
• E. 0.981

E. 0.981

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