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Practice Final Exam 1

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module is a practice final for an associated elementary statistics textbook, Collaborative Statistics.

Questions 1-2 refer to the following:

An experiment consists of tossing two 12-sided dice (the numbers 1-12 are printed on the sides of each dice).

  • Let Event AA = both dice show an even number
  • Let Event BB = both dice show a number more than 8

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.

Exercise 2

Find P ( A | B ) P ( A | B )

  • A. 2 4 2 4
  • B. 16 144 16 144
  • C. 4 16 4 16
  • D. 2 144 2 144

Solution

C: 4 16 4 16

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 means 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.

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

Solution

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.

Table 2
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

Solution

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

Solution

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

Solution

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 mean 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's-t
  • C. Normal
  • D. Uniform

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. conclude 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. conclude 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. conclude 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. conclude 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: conclude 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 to:

  • A. reject H o H o
  • B. not reject H o H o
  • C. There is not enough information given to conduct the hypothesis test

Solution

B: 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. Impossible to determine

Solution

C: Iris

Questions 15 – 16 refer to the following:

The following 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 normal. The null hypothesis is that the mean price of 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's-t
  • D. Exponential

Solution

C: Student's-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

Sara, a statistics student, wanted to determine the mean 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 18

A clothing store would use which measure of the center of data when placing orders for the typical "middle" customer?

  • A. Mean
  • B. Median
  • C. Mode
  • D. IQR

Solution

B: Median

Exercise 19

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.

Solution

A: the probability that an outcome of the data will happen purely by chance when the null hypothesis is true.

Questions 20 - 22 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. Each of her classes are the same size. 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 20

Combined with convenience sampling, what other sampling technique did Maria use?

  • A. simple random
  • B. systematic
  • C. cluster
  • D. stratified

Solution

D: stratified

Exercise 21

How many students come to campus for classes 4 days a week?

  • A. 49
  • B. 25
  • C. 30
  • D. 13

Solution

B: 25

Exercise 22

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 23

Construct a 95% Confidence Interval for the true population mean 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 24

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 mean 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 25

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 26

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. cannot be determined

Solution

C: 0.6321

Exercise 27

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 28

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 29

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 = mean 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 30

Suppose that Phi Beta Kappa honors the top 1% of college and university seniors. Assume that grade point means (G.P.A.) at a certain college are normally distributed with a 2.5 mean 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

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 31

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 32

In linear regression, which is the best possible SSE?

  • A. 13.46
  • B. 18.22
  • C. 24.05
  • D. 16.33

Solution

A: 13.46

Exercise 33

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 34-36 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 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 34

The distribution for the test is:

  • A. Chi 2 8 Chi 2 8
  • B. Chi 2 3 Chi 2 3
  • C. t 721 t 721
  • D. N ( 0 ,1 ) N ( 0 ,1 )

Solution

B: Chi 2 3 Chi 2 3

Exercise 35

The expected number of female who choose Finance is :

  • A. 37
  • B. 61
  • C. 60
  • D. 70

Solution

D: 70

Exercise 36

The p-value is 0.0127 and the level of significance is 0.05. The conclusion to the test is:

  • A. There is insufficient evidence to conclude that the choice of major and the gender of the student are not independent of each other.
  • B. There is sufficient evidence to conclude that the choice of major and the gender of the student are not independent of each other.
  • C. There is sufficient evidence to conclude that students find Economics very hard.
  • D. There is in sufficient evidence to conclude that more females prefer Administration than males.

Solution

B: There is sufficient evidence to conclude that the choice of major and the gender of the student are not independent of each other.

Exercise 37

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? Which kind of test is it?

  • 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

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