Deck 11: Comparisons Involving Proportions and a Test of Independence

Question 1

A population where each element of the population is assigned to one and only one of several classes or categories is a

A)multinomial population
B)Poisson population
C)normal population
D)None of these alternatives is correct.

Answer 1

multinomial population

Question 2

If a hypothesis is rejected at 95% confidence,

A)it must also be rejected at the 99% confidence
B)it must also be rejected at the 90% confidence
C)it will sometimes be rejected and sometimes not be rejected at the 90% confidence
D)Not enough information is given to answer this question.

Answer 2

it must also be rejected at the 90% confidence

Question 3

The purpose of the hypothesis test for proportions of a multinomial population is to determine whether the actual proportions

A)are all equal
B)follow a normal distribution
C)are different than the hypothesized proportions
D)follow a chi-square distribution

Answer 3

are different than the hypothesized proportions

Question 4

The sampling distribution for a goodness of fit test is the

A)Poisson distribution
B)t distribution
C)normal distribution
D)chi-square distribution

Question 5

Both the hypothesis test for proportions of a multinomial population and the test of independence employ the

A)F distribution
B)t distribution
C)normal distribution
D)chi-square distribution

Question 6

The sampling distribution of is approximated by a

A)normal distribution
B)t distribution with n₁ + n₂ degrees of freedom
C)t distribution with n₁ + n₂ - 1 degrees of freedom
D)t distribution with n₁ + n₂ + 2 degrees of freedom

Question 7

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

A)null hypothesis should state p₁ - p₂ $\gt$ 0
B)null hypothesis should state p₁ - p₂ $\ge$ 0
C)alternative hypothesis should state p₁ - p₂ $\gt$ 0
D)alternative hypothesis should state p₁ - p₂ $\lt$ 0

Question 8

In the case of the test of independence, the number of degrees of freedom for the appropriate chi-square distribution is computed as

A)k - 1
B)k - 2
C)(r - 1)(c - 1)
D)rc - 2

Question 9

The assumptions for the multinomial experiment parallel those for the binomial experiment with the exception that for the multinomial

A)there are more trials
B)the probability of each outcome can change from trial to trial
C)there are three or more outcomes per trial
D)the trials are not independent

Question 10

Assume we are interested in determining whether the proportion of voters planning to vote for candidate C (p_C) is significantly less than the proportion of voters planning to vote for candidate B (p_B). The correct null hypothesis for testing the above is

A)Ho: p_C - p_B $\le$ 0
B)Ho: p_C - p_B $\lt$ 0
C)Ho: p_C - p_B $\neq$ 0
D)Ho: p_C - p_B $\ge$ 0

Question 11

The properties of a multinomial experiment include all of the following except

A)the experiment consists of a sequence of n identical trials
B)three or more outcomes are possible on each trial
C)the probability of each outcome can change from trial to trial
D)the trials are independent

Question 12

A goodness of fit test is always conducted as a

A)lower-tail test
B)upper-tail test
C)middle test
D)None of these alternatives is correct.

Question 13

In conducting a hypothesis test about p₁ - p₂, any of the following approaches can be used except

A)comparing the observed frequencies to the expected frequencies
B)comparing the p-value to $\alpha$
C)comparing the hypothesized difference to the confidence interval
D)comparing the test statistic to the critical value

Question 14

If the p-value is less than $\alpha$ ,

A)the alternative hypothesis is rejected
B)the null hypothesis is rejected
C)the null hypothesis will sometimes be rejected and sometimes not be rejected depending on the sample size
D)Not enough information is given to answer this question.

Question 15

The test of independence presented in our textbook requires that there be

A)two variables, each having two outcomes
B)two variables, each having two or more outcomes
C)two or more variables, each having two outcomes
D)two or more variables, each having two or more outcomes

Question 16

Both the hypothesis test for proportions of a multinomial population and the test of independence focus on the difference between

A)sample means and population means
B)observed frequencies and expected frequencies
C)two population proportions
D)two interval estimates

Question 17

The test statistic for the chi-square tests in our textbook requires, for each category, an expected frequency of at least

A)2
B)5
C)10
D)30

Question 18

The test for goodness of fit

A)is always a one-tail test with the rejection region occurring in the upper tail
B)is always a one-tail test with the rejection region occurring in the lower tail
C)is always a two-tail test
D)can be a one-tail or two-tail test

Question 19

Which of the following does not need to be known in order to compute the p-value?

A)knowledge of whether the test is one-tailed or two-tailed
B)the value of the test statistic
C)the level of significance
D)All of the information provided is necessary.

Question 20

In a two-tailed hypothesis test the test statistic is determined to be z =-2.5. The p-value for this test

A)is 0.0062
B)is 0.0124
C)is 0.4938
D)cannot be determined, since the level of confidence is not given.

Question 21

Exhibit 11-3
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.

Refer to Exhibit 11-3. The 95% confidence interval for the difference between the two proportions is

A)384 to 450
B)0.48 to 0.5
C)0.028 to 0.068
D)-0.068 to 0.028

Question 22

Exhibit 11-3
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.

Refer to Exhibit 11-3. The standard error of is

A)0.48
B)0.50
C)0.03
D)0.0243

Question 23

Exhibit 11-1
The results of a recent poll on the preference of shoppers regarding two products are shown below.

Refer to Exhibit 11-1. The point estimate for the difference between the two population proportions in favor of this product is

A)52
B)100
C)0.44
D)0.02

Question 24

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

A)contingency test
B)probability test
C)goodness of fit test
D)None of these alternatives is correct.

Question 25

Exhibit 11-1
The results of a recent poll on the preference of shoppers regarding two products are shown below.

Refer to Exhibit 11-1. The 95% confidence interval estimate for the difference between the populations favoring the products is

A)-0.024 to 0.064
B)0.6 to 0.7
C)0.024 to 0.7
D)0.02 to 0.3

Question 26

Exhibit 11-1
The results of a recent poll on the preference of shoppers regarding two products are shown below.

Refer to Exhibit 11-1. The standard error of is

A)52
B)0.044
C)0.0225
D)100

Question 27

The degrees of freedom for a contingency table with 12 rows and 12 columns is

A)144
B)121
C)12
D)120

Question 28

Exhibit 11-4
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
Refer to Exhibit 11-4. The calculated value for the test statistic equals

A)2
B)-2
C)20
D)4

Question 29

The degrees of freedom for a contingency table with 10 rows and 11 columns is

A)100
B)110
C)21
D)90

Question 30

Exhibit 11-2
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.


-Refer to Exhibit 11-2 and let p_U represent the proportion under and p_O the proportion over the age of 18. The null hypothesis is

A)p_U - p_O $\le$ 0
B)p_U - p_O $\ge$ 0
C)p_U F-p_O $\neq$ 0
D)p_U- p_O = 0

Question 31

Exhibit 11-1
The results of a recent poll on the preference of shoppers regarding two products are shown below.

Refer to Exhibit 11-1. At 95% confidence, the margin of error is

A)0.064
B)0.044
C)0.0225
D)52

Question 32

Exhibit 11-3
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.

Refer to Exhibit 11-3. The point estimate for the difference between the proportions is

A)-0.02
B)0.048
C)100
D)66

Question 33

Exhibit 11-2
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Refer to Exhibit 11-2. The test statistic is

A)0.96
B)1.96
C)2.96
D)3.96

Question 34

Exhibit 11-4
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
Refer to Exhibit 11-4. The expected frequency for each group is

A)0.333
B)0.50
C)1/3
D)50

Question 35

Exhibit 11-2
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Refer to Exhibit 11-2. The p-value is

A)less than 0.001
B)more than 0.10
C)0.0228
D)0.3

Question 36

The degrees of freedom for a contingency table with 6 rows and 3 columns is

A)18
B)6
C)4
D)10

Question 37

In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be

A)at least 5
B)at least 10
C)no more than 5
D)less than 2

Question 38

Exhibit 11-2
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Refer to Exhibit 11-2. The pooled proportion is

A)0.305
B)0.300
C)0.027
D)0.450

Question 39

An important application of the chi-square distribution is

A)making inferences about a single population variance
B)testing for goodness of fit
C)testing for the independence of two variables
D)All of these alternatives are correct.

Question 40

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is

A)n -1
B)k - 1
C)number of rows minus 1 times number of columns minus 1
D)a chi-square distribution is not used

Question 41

Exhibit 11-7
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-7. The expected frequency for the Business College is

A)0.3
B)0.35
C)90
D)105

Question 42

Exhibit 11-7
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-7. The conclusion of the test is that the

A)proportions have changed significantly
B)proportions have not changed significantly
C)test is inconclusive
D)None of these alternatives is correct.

Question 43

Exhibit 11-5
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
Refer to Exhibit 11-5. The p-value is

A)less than .005
B)between .025 and 0.05
C)between .05 and 0.1
D)greater than 0.1

Question 44

Exhibit 11-7
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-7. The p-value is

A)greater than 0.1
B)between 0.05 and 0.1
C)between 0.025 and 0.05
D)between 0.01 and .025

Question 45

Exhibit 11-7
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-7. The calculated value for the test statistic equals

A)0.01
B)0.75
C)4.29
D)4.38

Question 46

Exhibit 11-4
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
Refer to Exhibit 11-4. The p-value is

A)larger than 0.1
B)less than 0.1
C)less than 0.05
D)larger than 0.9

Question 47

Exhibit 11-5
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
Refer to Exhibit 11-5. The expected frequency of seniors is

A)60
B)20%
C)68
D)64

Question 48

Exhibit 11-6
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 11-6. The test statistic is

A)10.08
B)54.02
C)1.96
D)1.645

Question 49

Exhibit 11-6
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 11-6. The expected frequency of those who received medication and were cured is

A)70
B)150
C)28
D)48

Question 50

Exhibit 11-4
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
Refer to Exhibit 11-4. The conclusion of the test (at 95% confidence) is that the

A)distribution is uniform
B)distribution is not uniform
C)test is inconclusive
D)None of these alternatives is correct.

Question 51

Exhibit 11-5
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
Refer to Exhibit 11-5. At 95% confidence, the null hypothesis

A)should not be rejected
B)should be rejected
C)was designed wrong
D)None of these alternatives is correct.

Question 52

Exhibit 11-5
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
Refer to Exhibit 11-5. The expected number of freshmen is

A)83
B)90
C)30
D)10

Question 53

Exhibit 11-7
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-7. This problem is an example of a

A)normally distributed variable
B)test for independence
C)Poisson distributed variable
D)multinomial population

Question 54

Exhibit 11-4
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
Refer to Exhibit 11-4. The number of degrees of freedom associated with this problem is

A)150
B)149
C)2
D)3

Question 55

Exhibit 11-5
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
Refer to Exhibit 11-5. The calculated value for the test statistic equals

A)0.5444
B)300
C)1.6615
D)6.6615

Question 56

Exhibit 11-8
The table below gives beverage preferences for random samples of teens and adults.
We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 11-8. With a .05 level of significance, the critical value for the test is

A)1.645
B)7.815
C)14.067
D)15.507

Question 57

Exhibit 11-6
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 11-6. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

A)3.84
B)7.81
C)5.99
D)9.34

Question 58

Exhibit 11-6
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 11-6. The number of degrees of freedom associated with this problem is

A)4
B)149
C)1
D)3

Question 59

Exhibit 11-6
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 11-6. The p-value is

A)less than .005
B)between .005 and .01
C)between .01 and .025
D)between .025 and .05

Question 60

Exhibit 11-7
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-7. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

A)1.645
B)1.96
C)5.991
D)7.815

Question 61

Exhibit 11-8
The table below gives beverage preferences for random samples of teens and adults.
We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 11-8. The expected number of adults who prefer coffee is

A)0.25
B)0.33
C)150
D)200

Question 62

Of 150 Chattanooga residents surveyed, 60 indicated that they participated in a recycling program. In Knoxville, 120 residents were surveyed and 36 claimed to recycle.

A)Determine a 95% confidence interval estimate for the difference between the proportions of residents recycling in the two cities.
B)From your answer in Part a, is there sufficient evidence to conclude that there is a significant difference in the proportion of residents participating in a recycling program?

Question 63

The degrees of freedom for a chi-square test involving 5 proportions are

A)3
B)4
C)5
D)6

Question 64

Babies weighing less than 5.5 pounds at birth are considered "low-birth-weight babies." In the United States, 7.6% of newborns are low-birth-weight babies. The following information was accumulated from samples of new births taken from two counties.

a.Develop a 95% confidence interval estimate for the difference between the proportions of low-weight babies in the two counties.
a. Do not perform any test.
b.Is there conclusive evidence that one of the proportions is significantly more than the other? If yes, which county? Explain, using the results of Part

Question 65

Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president.
a.Compute the test statistic.
b.At alpha = .05, test to see if there is a significant difference between the proportions of females and males who plan to vote for the incumbent president. (Use the p-value approach.)

Question 66

Exhibit 11-8
The table below gives beverage preferences for random samples of teens and adults.
We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 11-8. The p-value is

A)between .1 and .05
B)between .05 and .025
C)between .025 and .01
D)less than 0.005

Question 67

If the chi-square test indicates that there is no difference between two proportions, this indicates that

A)the two variables are correlated
B)the two variables are independent
C)the two variables are dependent
D)there is a relationship between the two variables

Question 68

In a random sample of 200 Republicans, 160 opposed the new tax laws. While in a sample of 120 Democrats, 84 opposed the new tax laws. Determine a 95% confidence interval estimate for the difference between the proportions of Republicans and Democrats opposed to this new law.

Question 69

The results of a recent poll on the preference of voters regarding the presidential candidates are shown below.

a.Develop a 90% confidence interval estimate for the difference between the proportions of voters favoring each candidate.
b.Does your confidence interval provide conclusive evidence that one of the candidates is favored more? Explain.

Question 70

Exhibit 11-8
The table below gives beverage preferences for random samples of teens and adults.
We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 11-8. The test statistic for this test of independence is

A)0
B)8.4
C)62.5
D)82.5

Question 71

Of 200 UTC seniors surveyed, 60 were planning on attending Graduate School. At UTK, 400 seniors were surveyed; and 100 indicated that they were planning to attend Graduate School.
a.Determine a 95% confidence interval estimate for the difference between the proportions of seniors at the two universities that were planning to attend Graduate School.
b.Is there conclusive evidence to prove that the proportion of students from UTC who plan to go to Graduate School is significantly more than those from UTK? Explain.

Question 72

All of the following tests follow a chi-square distribution except

A)test of independence of two variables
B)test for the difference between two proportions
C)test for proportions of a multinomial population
D)test for the difference between two means

Question 73

When conducting a good of fit test, the expected frequencies for the multinomial population are based on the

A)chi-square distribution
B)normal distribution
C)null hypothesis
D)alternative hypothesis

Question 74

Among a sample of 50 MDs (medical doctors) in the city of Memphis, Tennessee, 10 indicated they make house calls; while among a sample of 100 MDs in Atlanta, Georgia, 18 said they make house calls. Determine a 95% interval estimate for the difference between the proportions of doctors who make house calls in the two cities.

Question 75

When a category in a contingency table has an expected frequency of less than five,

A)switch from a one-tailed test to a two-tailed test
B)conclude that the two variables are independent
C)double the expected frequency in every category
D)combine two adjacent categories to obtain an expected frequency of five or more

Question 76

In a sample of 40 Democrats, 6 opposed the President's foreign policy, while of 50 Republicans, 8 were opposed to his policy. Determine a 90% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

Question 77

During the primary elections of 2008, candidate A showed the following pre-election voter support in Tennessee and Mississippi.

a.Develop a 95% confidence interval estimate for the difference between the proportion of voters favoring candidate A in the two states.
b.Is there conclusive evidence that one of the two states had a larger proportion of voters' support? If yes, which state? Explain.

Question 78

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five ago. Results are summarized below. Has the proportion increased significantly? Let $\alpha$ = 0.05.

Question 79

From production line A, a sample of 500 items is selected at random; and it is determined that 30 items are defective. In a sample of 300 items from production process B (which produces identical items to line A), there are 12 defective items. Determine a 95% confidence interval estimate for the difference between the proportions of defectives in the two lines.

Question 80

During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi.

a.We want to determine whether or not the proportions of voters favoring the Democratic candidate were the same in both states. Provide the hypotheses.
b.Compute the test statistic.
c.Determine the p-value; and at 95% confidence, test the above hypotheses.