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Review Questions

Module by: Roberta Bloom. E-mail the author

Based on: F Distribution and ANOVA: Review by Susan Dean, Barbara Illowsky, Ph.D.

Summary: Copy of Review Questions module m17070 (http://cnx.org/content/ m17070/) from Collaborative Statistics by Dean and Illowsky http://cnx.org/content/col10522/ , 12/18/2008 . The FORMAT only of the question numbering has been changed.

The next two questions 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 1: REVIEW QUESTION 1

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

Solution

REVIEW QUESTION 1 Solution : 0.02

Exercise 2: REVIEW QUESTION 2

Out of the years with water rationing, find the probability that there is a drought.

Solution

REVIEW QUESTION 2 Solution : 0.40

The next three questions refer to the following survey:

Table 1: Favorite Type of Pie by Gender
  apple pumpkin pecan
female 40 10 30
male 20 30 10

Exercise 3: REVIEW QUESTION 3

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

Solution

REVIEW QUESTION 3 Solution : 100 140 100 140 size 12{ { { size 8{"100"} } over { size 8{"140"} } } } {}

Exercise 4: REVIEW QUESTION 4

Suppose that one male is randomly chosen. Find the probability his favorite pie is pecan.

Solution

REVIEW QUESTION 4 Solution 10 60 10 60 size 12{ { { size 8{"10"} } over { size 8{"60"} } } } {}

Exercise 5: REVIEW QUESTION 5

Conduct a hypothesis test to determine if favorite pie type and gender are independent.

Solution

REVIEW QUESTION 5 Solution : p-value=0p-value=0 ; Reject null hypothesis ; Conclude dependent events

The next two questions 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.

Exercise 6: REVIEW QUESTION 6

We randomly survey 14 people. On average, how many people do we expect to watch the news at least once per week?

Solution

REVIEW QUESTION 6 Solution : 8.4

Exercise 7: REVIEW QUESTION 7

We randomly survey 14 people. Of interest is the number that watch the news at least once per week. State the distribution of XX. XX ~

Solution

REVIEW QUESTION 7 Solution : B 14 , 0 . 60 B 14 , 0 . 60 size 12{B left ("14",0 "." "60" right )} {}

Exercise 8: REVIEW QUESTION 8

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

Figure 1
Histogram with 7 bars.

  • A. Chi-Square
  • B. Geometric
  • C. Uniform
  • D. Binomial

Solution

REVIEW QUESTION 8 Solution : D

Exercise 9

REVIEW QUESTION 9 Removed

The next three questions refer to the following situation:

The amount of money a customer spends in one trip to the supermarket is known to have an exponential distribution. Suppose the average amount of money a customer spends in one trip to the supermarket is $72.

Exercise 10: REVIEW QUESTION 10

Find the probability that one customer spends less than $72 in one trip to the supermarket?

Solution

REVIEW QUESTION 10 Solution : 0.6321

Exercise 11: REVIEW QUESTION 11

Suppose 5 customers pool their money. (They are poor college students.) How much money altogether would you expect the 5 customers to spend in one trip to the supermarket (in dollars)?

Solution

REVIEW QUESTION 11 Solution : $360

Exercise 12: REVIEW QUESTION 12

State the distribution to use is if you want to find the probability that the average amount spent by 5 customers in one trip to the supermarket is less than $60.

Solution

REVIEW QUESTION 12 Solution : N 72 , 72 5 N 72 , 72 5 size 12{N left ("72", { { size 8{"72"} } over { size 8{ sqrt {5} } } } right )} {}

Exercise 13: REVIEW QUESTION 13

A math exam was given to all the fifth grade children attending Country School. Two random samples of scores were taken. The null hypothesis is that the average math scores for boys and girls in fifth grade are the same. Conduct a hypothesis test.

Table 2
  n n size 12{n} {} x ¯ x ¯ size 12{ {overline {x}} } {} s 2 s 2 size 12{s rSup { size 8{2} } } {}
Boys 55 82 29
Girls 60 86 46

Solution

REVIEW QUESTION 13 Solution : p-value=0.0006p-value=0.0006; Reject null; Conclude averages are not equal

Exercise 14: REVIEW QUESTION 14

In a survey of 80 males, 55 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. Conduct a hypothesis test.

Solution

REVIEW QUESTION 14 Solution : p-value=0p-value=0; Reject null; Conclude proportion of males is higher

Exercise 15: REVIEW QUESTION 15

Which of the following is preferable when designing a hypothesis test?

  • A. Maximize αα size 12{α} {} and minimize ββ size 12{β} {}
  • B. Minimize αα size 12{α} {} and maximize ββ size 12{β} {}
  • C. Maximize αα size 12{α} {} and ββ size 12{β} {}
  • D. Minimize αα size 12{α} {} and ββ size 12{β} {}

Solution

REVIEW QUESTION 15 Solution : D

The next three questions refer to the following situation:

120 people were surveyed as to their favorite beverage (non-alcoholic). The results are below.

Table 3: Preferred Beverage by Age
  0 – 9 10 – 19 20 – 29 30 +   Totals
Milk 14 10 6 0 30
Soda 3 8 26 15 52
Juice 7 12 12 7 38
Totals 24 30 44 22 120

Exercise 16: REVIEW QUESTION 16

Are the events of milk and 30+:

  • a. Independent events? Justify your answer.
  • b. Mutually exclusive events? Justify your answer.

Solution

REVIEW QUESTION 16 Solution

  • a. No
  • b. Yes, P Mand 30 + = 0 P Mand 30 + = 0 size 12{P left ( ital "Mand""30"+{} right )=0} {}

Exercise 17: REVIEW QUESTION 17

Suppose that one person is randomly chosen. Find the probability that person is 10 – 19 given that he/she prefers juice.

Solution

REVIEW QUESTION 17 Solution : 12 38 12 38 size 12{ { { size 8{"12"} } over { size 8{"38"} } } } {}

Exercise 18: REVIEW QUESTION 18

Are Preferred Beverage and Age independent events? Conduct a hypothesis test.

Solution

REVIEW QUESTION 18 Solution : No; p-value=0p-value=0

Exercise 19: REVIEW QUESTION 19

Given the following histogram, which distribution is the data most likely to come from?

Figure 2
Histogram with 8 bars.

  • A. uniform
  • B. exponential
  • C. normal
  • D. chi-square

Solution

REVIEW QUESTION 19 Solution : A

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