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Elementary Statistics: Practice Final Exam 2

Summary: Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

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Practice Final Exam 2

Exercise 1

A study was done to determine the proportion of teenagers that own a car. The true proportion of teenagers that own a car is the:

• statistic
• parameter
• population
• variable

parameter

Table 1
value frequency
0 1
1 4
2 7
3 9
6 4

Exercise 2

The box plot for the data is:

(A)

Exercise 3

If 6 were added to each value, the 15th percentile would be:

• 6
• 1
• 7
• 8

6

Questions 4 - 5 refer to the following situation:

Suppose that the probability of a drought in any independent year is 20%. Out of those years in which a drought occurs, the probability of water rationing is 10%. However, in any year, the probability of water rationing is 5%.

Exercise 4

What is the probability of both a drought and water rationing occurring?

• 0.05
• 0.01
• 0.02
• 0.30

0.02

Exercise 5

Which of the following is true?

• drought and water rationing are independent events
• drought and water rationing are mutually exclusive events
• none of the above

Solution

none of the above

Questions 6 - 7 refer to the following situation:

Suppose that a survey yielded the following data:

Table 2: Favorite Pie Type
gender apple pumpkin pecan
female 40 10 30
male 20 30 10

Exercise 6

Suppose that one individual is randomly chosen. The probability that the person’s favorite pie is apple or the person is male is:

• 40 60 40 60
• 60 140 60 140
• 120 140 120 140
• 100 140 100 140

100 140 100 140

Exercise 7

Suppose H o H o is: Favorite pie type and gender are independent.

The p-value is:

• ≈ 0
• 1
• 0.05
• cannot be determined

≈ 0

Questions 8 - 9 refer to the following situation:

Let’s say that the probability that an adult watches the news at least once per week is 0.60. We randomly survey 14 people. Of interest is the number that watch the news at least once per week.

Exercise 8

Which of the following statements is FALSE?

• X ~ B 14 0.60 X~B 14 0.60
• The values for xx are: { 1 ,2 ,3 ,... , 14 } { 1 ,2 ,3 ,... , 14 }
• μ = 8.4 μ=8.4
• P ( X = 5 ) = 0.0408P(X=5)=0.0408

Solution

The values for xx are: { 1 ,2 ,3 ,... , 14 } { 1 ,2 ,3 ,... , 14 }

Exercise 9

Find the probability that at least 6 adults watch the news.

• 6 14 6 14
• 0.8499
• 0.9417
• 0.6429

0.9417

Exercise 10

Histogram Goes Here

The following histogram is most likely to be a result of sampling from which distribution?

• Chi-Square
• Exponential
• Uniform
• Binomial

Solution

Binomial

The ages of campus day and evening students is known to be normally distributed. A sample of 6 campus day and evening students reported their ages (in years) as: { 18 ,35 ,27 ,45 20 , 20 } { 18 ,35 ,27 ,45 20 , 20 }

Exercise 11

What is the probability that the average of 6 ages of randomly chosen students is less than 25 years?

• 0. 2935
• 0. 4099
• 0. 4052
• 0. 2810

.2810

Exercise 12

If a normally distributed random variable has µ = 0 and σ = 1 , then 97.5% of the population values lie above:

• - 1.96
• 1.96
• 1
• - 1

-1.96

• 0.6321
• 0.5000
• 0.3714
• 1

0.6321

Exercise 14

How much money altogether would you expect next 5 customers to spend in one trip to the supermarket (in dollars)?

• 72
• 725 5 725 5
• 5184
• 360

360

• 16
• 0. 2
• 1
• 0. 95

0.2

Exercise 23

If P ( Z < z α ) = 0P(Z< z α )=0. 1587 where Z ~ N 0 1 Z~N 0 1 , then αα is equal to:

• - 1
• 0. 1587
• 0. 8413
• 1

-1

Exercise 24

A professor tested 35 students to determine their entering skills. At the end of the term, after completing the course, the same test was administered to the same 25 students to study their improvement. This would be a test of:

• independent groups
• 2 proportions
• dependent groups
• exclusive groups

dependent groups

Exercise 25

A math exam was given to all the third grade children attending ABC School. Two random samples of scores were taken.

Table 4
n x¯x¯ s
Boys 55 82 5
Girls 60 86 7

Which of the following correctly describes the results of a hypothesis test of the claim, “There is a difference between the mean scores obtained by third grade girls and boys at the 5 % level of significance”?

• Do not reject H o H o . There is no difference in the mean scores.
• Do not reject H o H o . There is a difference in the mean scores.
• Reject H o H o . There is no difference in the mean scores.
• Reject H o H o . There is a difference in the mean scores.

Solution

Reject H o H o . There is a difference in the mean scores.es.

Exercise 26

In a survey of 80 males, 45 had played an organized sport growing up. Of the 70 females surveyed, 25 had played an organized sport growing up. We are interested in whether the proportion for males is higher than the proportion for females. The correct conclusion is:

• The proportion for males is the same as the proportion for females.
• The proportion for males is not the same as the proportion for females.
• The proportion for males is higher than the proportion for females.
• Not enough information to determine.

Solution

The proportion for males is higher than the proportion for females.

Exercise 27

From past experience, a statistics teacher has found that the average score on a midterm is 81 with a standard deviation of 5.2. This term, a class of 49 students had a standard deviation of 5 on the midterm. Do the data indicate that we should reject the teacher’s claim that the standard deviation is 5.2? Use α = 0.05 α=0.05.

• Yes
• No
• Not enough information given to solve the problem

No

Exercise 28

Three loading machines are being compared. Machine I took 31 minutes to load packages. Machine II took 28 minutes to load packages. Machine III took 29 minutes to load packages. The expected time for any machine to load packages is 29 minutes. Find the p-value when testing that the loading times are the same.

• the p–value is close to 0
• p–value is close to 1
• Not enough information given to solve the problem

Solution

Not enough information given to solve the problem

Questions 29 - 31 refer to the following situation:

A corporation has offices in different parts of the country. It has gathered the following information concerning the number of bathrooms and the number of employees at seven sites:

 Number of employees x Number of bathrooms y 650 730 810 900 1020 1070 1150 40 50 54 61 82 110 121

Exercise 29

Is there a correlation between the number of employees and the number of bathrooms significant?

• Yes
• No
• Not enough information to answer question

No

Exercise 30

The linear regression equation is:

• y ̂ = 0.0094 79.96 x y ̂ =0.009479.96x
• y ̂ = 79.96 x + 0.0094 y ̂ =79.96x+0.0094
• y ̂ = 79.96 x - 0.0094 y ̂ =79.96x-0.0094
• y ̂ = 0.0094 + 79.96 x y ̂ =0.0094+79.96x

Solution

y ̂ = 79.96 x - 0.0094 y ̂ =79.96x-0.0094

Exercise 31

If a site has 1150 employees, approximately how many bathrooms should it have?

• 69
• 121
• 101
• 86

69

Exercise 32

Suppose that a sample of size 10 was collected, with ***SORRY, THIS MEDIA TYPE IS NOT SUPPORTED.*** = 4.4 and s = 1.4 .

H o H o : σ 2 σ 2 = 1.6 vs. H a H a : σ 2 σ 2 ≠ 1.6

 ***SORRY, THIS MEDIA TYPE IS NOT SUPPORTED.*** ***SORRY, THIS MEDIA TYPE IS NOT SUPPORTED.*** ***SORRY, THIS MEDIA TYPE IS NOT SUPPORTED.*** ***SORRY, THIS MEDIA TYPE IS NOT SUPPORTED.***

(c)

Exercise 33

64 backpackers were asked the number of days their latest backpacking trip was. The number of days is given in the table below:

 # of days Frequency 1 2 3 4 5 6 7 8 5 9 6 12 7 10 5 10

Conduct an appropriate test to determine if the distribution is uniform.

• The p–value is > 0.10 , the distribution is uniform.
• The p–value is < 0.01 , the distribution is uniform.
• The p–value is between 0.01 and 0.10, but without α there is not enough information
• There is no such test that can be conducted.

Solution

The p–value is < 0.01 , the distribution is uniform.

Exercise 34

­Which of the following assumptions is made when using one-way ANOVA?

• The populations from which the samples are selected have different distributions.
• The sample sizes are large.
• The test is to determine if the different groups have the same averages.
• There is a correlation between the factors of the experiment.

Solution

The test is to determine if the different groups have the same averages.

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