# Quiz 11: Comparisons Involving Proportions and a Test of Independence

Statistics

Q 1Q 1

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 < 0
B) null hypothesis should state P1 - P2 > 0
C) alternative hypothesis should state P1 - P2 > 0
D) alternative hypothesis should state P1 - P2 < 0

Free

Multiple Choice

C

Q 2Q 2

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

Free

Multiple Choice

A

Q 3Q 3

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.

Free

Multiple Choice

A

Q 4Q 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

Free

Multiple Choice

Q 5Q 5

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.

Free

Multiple Choice

Q 6Q 6

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.

Free

Multiple Choice

Q 7Q 7

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

Free

Multiple Choice

Q 8Q 8

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

Free

Multiple Choice

Q 9Q 9

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.

Free

Multiple Choice

Q 10Q 10

The degrees of freedom for a contingency table with 12 rows and 12 columns is
A) 144
B) 121
C) 12
D) 120

Free

Multiple Choice

Q 11Q 11

The degrees of freedom for a contingency table with 6 rows and 3 columns is
A) 18
B) 15
C) 6
D) 10

Free

Multiple Choice

Q 12Q 12

The degrees of freedom for a contingency table with 10 rows and 11 columns is
A) 100
B) 110
C) 21
D) 90

Free

Multiple Choice

Q 13Q 13

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
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 11-1. The expected frequency for each group is
A) 0.333
B) 0.50
C) 1/3
D) 50

Free

Multiple Choice

Q 14Q 14

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
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 11-1. The calculated value for the test statistic equals
A) 2
B) -2
C) 20
D) 4

Free

Multiple Choice

Q 15Q 15

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
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 11-1. The number of degrees of freedom associated with this problem is
A) 150
B) 149
C) 2
D) 3

Free

Multiple Choice

Q 16Q 16

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
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 11-1. The p-value is
A) larger than 0.1
B) less than 0.1
C) less than 0.05
D) larger than 0.9

Free

Multiple Choice

Q 17Q 17

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
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 11-1. 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.

Free

Multiple Choice

Q 18Q 18

Exhibit 11-2
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 11-2. The expected number of freshmen is
A) 83
B) 90
C) 30
D) 10

Free

Multiple Choice

Q 19Q 19

Exhibit 11-2
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 11-2. The expected frequency of seniors is
A) 60
B) 20%
C) 68
D) 64

Free

Multiple Choice

Q 20Q 20

Exhibit 11-2
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 11-2. The calculated value for the test statistic equals
A) 0.5444
B) 300
C) 1.6615
D) 6.6615

Free

Multiple Choice

Q 21Q 21

Exhibit 11-2
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 11-2. 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

Free

Multiple Choice

Q 22Q 22

Exhibit 11-2
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 11-2. 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.

Free

Multiple Choice

Q 23Q 23

Exhibit 11-3
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 11-3. The expected frequency of those who received medication and were cured is
A) 70
B) 150
C) 28
D) 48

Free

Multiple Choice

Q 24Q 24

Exhibit 11-3
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 11-3. The test statistic is
A) 10.08
B) 54.02
C) 1.96
D) 1.645

Free

Multiple Choice

Q 25Q 25

Exhibit 11-3
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 11-3. The number of degrees of freedom associated with this problem is
A) 4
B) 149
C) 1
D) 3

Free

Multiple Choice

Q 26Q 26

Exhibit 11-3
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 11-3. 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

Free

Multiple Choice

Q 27Q 27

Exhibit 11-3
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 11-3. The p-value is
A) less than .005
B) between .005 and .01
C) between .01 and .025
D) between .025 and .05

Free

Multiple Choice

Q 28Q 28

Exhibit 11-4
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 11-4. This problem is an example of a
A) normally distributed variable
B) test for independence
C) Poisson distributed variable
D) multinomial population

Free

Multiple Choice

Q 29Q 29

Exhibit 11-4
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 11-4. The expected frequency for the Business College is
A) 0.3
B) 0.35
C) 90
D) 105

Free

Multiple Choice

Q 30Q 30

Exhibit 11-4
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 11-4. The calculated value for the test statistic equals
A) 0.01
B) 0.75
C) 4.29
D) 4.38

Free

Multiple Choice

Q 31Q 31

Exhibit 11-4
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 11-4. 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

Free

Multiple Choice

Q 32Q 32

Exhibit 11-4
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 11-4. 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

Free

Multiple Choice

Q 33Q 33

Exhibit 11-4
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 11-4. 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.

Free

Multiple Choice

Q 34Q 34

Exhibit 11-5
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 11-5. 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

Free

Multiple Choice

Q 35Q 35

Exhibit 11-5
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 11-5. The expected number of adults who prefer coffee is
A) 0.25
B) 0.33
C) 150
D) 200

Free

Multiple Choice

Q 36Q 36

Exhibit 11-5
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 11-5. The test statistic for this test of independence is
A) 0
B) 8.4
C) 62.5
D) 82.5

Free

Multiple Choice

Q 37Q 37

Exhibit 11-5
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 11-5. The p-value is
A) between .1 and .05
B) between .05 and .025
C) between .025 and .01
D) less than 0.005

Free

Multiple Choice

Q 38Q 38

Exhibit 11-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
-Refer to Exhibit 11-6. The expected frequency for each group is
A) 0.333
B) 0.50
C) 50
D) None of these alternatives is correct.

Free

Multiple Choice

Q 39Q 39

Exhibit 11-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
-Refer to Exhibit 11-6. The calculated value for the test statistic equals
A) 300
B) 4
C) 0
D) 8

Free

Multiple Choice

Q 40Q 40

Exhibit 11-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
-Refer to Exhibit 11-6. The number of degrees of freedom associated with this problem is
A) 2
B) 3
C) 300
D) 299

Free

Multiple Choice

Q 41Q 41

Exhibit 11-7
The results of a recent poll on the preference of shoppers regarding two products are shown below.
-Refer to Exhibit 11-7. 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

Free

Multiple Choice

Q 42Q 42

Exhibit 11-7
The results of a recent poll on the preference of shoppers regarding two products are shown below.
-Refer to Exhibit 11-7. At 95% confidence, the margin of error is
A) 0.064
B) 0.044
C) 0.0225
D) 52

Free

Multiple Choice

Q 43Q 43

Exhibit 11-7
The results of a recent poll on the preference of shoppers regarding two products are shown below.
-Refer to Exhibit 11-7. 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

Free

Multiple Choice

Q 44Q 44

Exhibit 11-8
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.
We are interested in determining if the accident proportions differ between the two age groups.
-Refer to Exhibit 11-8 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is
A) pu - po ≤ 0
B) pu - po ≥ 0
C) pu - po ≠ 0
D) pu - po = 0

Free

Multiple Choice

Q 45Q 45

Exhibit 11-8
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.
We are interested in determining if the accident proportions differ between the two age groups.
-Refer to Exhibit 11-8. The pooled proportion is
A) 0.305
B) 0.300
C) 0.027
D) 0.450

Free

Multiple Choice

Q 46Q 46

Exhibit 11-8
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.
We are interested in determining if the accident proportions differ between the two age groups.
-Refer to Exhibit 11-8. The test statistic is
A) 0.96
B) 1.96
C) 2.96
D) 3.96

Free

Multiple Choice

Q 47Q 47

Exhibit 11-8
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.
We are interested in determining if the accident proportions differ between the two age groups.
-Refer to Exhibit 11-8. The p-value is
A) less than 0.001
B) more than 0.10
C) 0.0228
D) 0.3

Free

Multiple Choice

Q 48Q 48

Exhibit 11-9
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 11-9. The point estimate for the difference between the proportions is
A) -0.02
B) 0.048
C) 100
D) 66

Free

Multiple Choice

Q 49Q 49

Exhibit 11-9
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 11-9. The standard error of is
A) 0.48
B) 0.50
C) 0.03
D) 0.0243

Free

Multiple Choice

Q 50Q 50

Exhibit 11-9
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 11-9. 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

Free

Multiple Choice

Q 51Q 51

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
-We are interested in testing the following hypotheses. H0: P1- P2 ≤ 0
Ha: P1- P2 > 0
The test statistic Z is computed to be 0.58. The p-value for this test is
A) 0.7190
B) 0.2810
C) 0.5620
D) 0.5800

Free

Multiple Choice

Q 52Q 52

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
-We are interested in testing the following hypotheses. H0: P1- P2 = 0 Ha: P1- P2 ≠ 0
The test statistic Z is computed to be 2.0. The p-value for this test is
A) 0.9772
B) 1.9544
C) 0.0228
D) 0.0456

Free

Multiple Choice

Q 53Q 53

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
-For a two-tailed test at 98.5% confidence, Z =
A) ± 2.17
B) ± 1.96
C) ± 2.98
D) ± 2.43

Free

Multiple Choice

Q 54Q 54

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
-For a one-tailed test lower tail) at 99.7% confidence, Z =
A) ± 1.86
B) - 2.75
C) ±1.96
D) -1.645

Free

Multiple Choice

Q 55Q 55

A comparative study of organic and conventionally grown produce was checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. Coli in organic vs. conventionally grown produce? Test at α = 0.10.

Free

Essay

Q 56Q 56

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 proportion 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.

Free

Essay

Q 57Q 57

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.)

Free

Essay

Q 58Q 58

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 proportion 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?

Free

Essay

Q 59Q 59

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

Free

Short Answer

Q 60Q 60

During the primary elections of 1996, candidate A showed the following pre-election voter support in Tennessee and Mississippi.
Voters Surveyed Voters Favoring Candidate A
Tennessee 500 295
Mississippi 700 357
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.

Free

Essay

Q 61Q 61

The results of a recent poll on the preference of voters regarding the presidential candidates are shown below.
Voters Surveyed
Voters Favoring This Candidate
Candidate A 200 150
Candidate B 300 195
a. Develop a 90% confidence interval estimate for the difference between the proportion of voters favoring each candidate.
b. Does your confidence interval provide conclusive evidence that one of the candidates is favored more? Explain.

Free

Essay

Q 62Q 62

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.

Free

Short Answer

Q 63Q 63

In a sample of 100 Republicans, 60 favored the President's anti-drug program. While in a sample of 150 Democrats, 84 favored his program. At 95% confidence, test to see if there is a significant difference in the proportions of the Democrats and the Republicans who favored the President's anti-drug program.

Free

Essay

Q 64Q 64

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.

Free

Short Answer

Q 65Q 65

During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi.
State Voters Surveyed
Voters Favoring the Democratic Candidate
Alabama 800 440
Mississippi 600 360
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.

Free

Essay

Q 66Q 66

The reliability of two types of machines used in the same manufacturing process is to be tested. The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials.
a. Give a point estimate for the difference between the population proportions of these machines.
b. Calculate the pooled estimate of the population proportion.
c. Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a .10 level of significance.

Free

Essay

Q 67Q 67

The results of a recent poll on the preference of voters regarding presidential candidates are shown below.
Candidate
Voters Surveyed
Voters Favoring This Candidate
A 400 192
B 450 225
At 95% confidence, test to determine whether or not there is a significant difference between the preferences for the two candidates.

Free

Essay

Q 68Q 68

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 proportion of defectives in the two lines.

Free

Short Answer

Q 69Q 69

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five years ago. Results are summarized below. Has the proportion increased significantly? Let α = 0.05.
Sample Size Number Considered
Themselves Overweight
Present Sample 300 150
Previous sample 275 121

Free

Essay

Q 70Q 70

Babies weighing less than 5.5 pounds at birth are considered "lowbirthweight 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-birth-weight babies in the two counties.
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 a). Do not perform any test.

Free

Essay

Q 71Q 71

In the last presidential election, before the candidates started their major campaigns, the percentages of registered voters who favored the various candidates were as follows.
After the major campaigns began, a random sample of 400 voters showed that 172 favored the Republican candidate; 164 were in favor of the Democratic candidate; and 64 favored the Independent candidate. We are interested in determining whether the proportion of voters who favored the various candidates had changed.
a. Compute the test statistic.
b. Using the p-value approach, test to see if the proportions have changed.
c. Using the critical value approach, test the hypotheses.

Free

Essay

Q 72Q 72

The results of a recent study regarding smoking and three types of illness are shown in the following table.
We are interested in determining whether or not illness is independent of smoking.
a. State the null and alternative hypotheses to be tested.
b. Show the contingency table of the expected frequencies.
c. Compute the test statistic.
d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude?
e. Determine the p-value and perform the test.

Free

Essay

Q 73Q 73

Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration.
We want to determine if the position in management is independent of field major) of concentration.
a. Compute the test statistic.
b. Using the p-value approach at 90% confidence, test to determine if management position is independent of major.
c. Using the critical value approach, test the hypotheses. Let α = 0.10.

Free

Essay

Q 74Q 74

From a poll of 800 television viewers, the following data have been accumulated as to their levels of education and their preference of television stations. We are interested in determining if the selection of a TV station is independent of the level of education.
a. State the null and the alternative hypotheses.
b. Show the contingency table of the expected frequencies.
c. Compute the test statistic.
d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test.
e. Determine the p-value and perform the test.

Free

Essay

Q 75Q 75

Before the start of the Winter Olympics, it was expected that the percentages of medals awarded to the top contenders to be as follows.
Midway through the Olympics, of the 120 medals awarded, the following distribution was observed.
We want to test to see if there is a significant difference between the expected and actual awards given.
a. Compute the test statistic.
b. Using the p-value approach, test to see if there is a significant difference between the expected and the actual values. Let α = .05.
c. At 95% confidence, test for a significant difference using the critical value approach.

Free

Essay

Q 76Q 76

A medical journal reported the following frequencies of deaths due to cardiac arrest for each day of the week:
Cardiac Death by Day of the Week
We want to determine whether the number of deaths is uniform over the week.
a. Compute the test statistic.
b. Using the p-value approach at 95% confidence, test for the uniformity of death over the week.
c. Using the critical value approach, perform the test for uniformity.

Free

Essay

Q 77Q 77

Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates would be as follows.
After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate, and 140 were undecided. We want to see if the proportion of voters has changed.
a. Compute the test statistic.
b. Use the p-value approach to test the hypotheses. Let α = .05.
c. Using the critical value approach, test the hypotheses. Let α = .05.

Free

Essay

Q 78Q 78

Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major:
We want to see if there has been a significant change in the number of students in each major.
a. Compute the test statistic.
b. Has there been any significant change in the number of students in each major between the last school year and this school year. Use the p-value approach and let α = .05.

Free

Essay

Q 79Q 79

In 2013, forty percent of the students at a major university were Business majors, 35% were Engineering majors and the rest of the students were majoring in other fields. In a sample of 600 students from the same university taken in 2014, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At 95% confidence, test to see if there has been a significant change in the proportions between 2013 and 2014.

Free

Essay

Q 80Q 80

Before the rush began for Christmas shopping, a department store had noted that the percentage of its customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store's credit card; 43 used a major credit card; and 61 paid cash. With α = 0.05, test to see if the methods of payment have changed during the Christmas rush.

Free

Essay

Q 81Q 81

A major automobile manufacturer claimed that the frequencies of repairs on all five models of its cars are the same. A sample of 200 repair services showed the following frequencies on the various makes of cars.
At α = 0.05, test the manufacturer's claim.

Free

Essay

Q 82Q 82

A lottery is conducted that involves the random selection of numbers from 0 to 4. To make sure that the lottery is fair, a sample of 250 was taken. The following results were obtained:
a. State the null and alternative hypotheses to be tested.
b. Compute the test statistic.
c. The null hypothesis is to be tested at the 5% level of significance. Determine the critical value from the table.
d. What do you conclude about the fairness of this lottery?

Free

Essay

Q 83Q 83

The makers of Compute-All know that in the past, 40% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 15% of their sales were from people who are over 50 years old. A sample of 300 customers was taken to see if the market shares had changed. In the sample, 100 of the people were under 30 years old, 150 people were between 30 and 50 years old, and 50 people were over 50 years old.
a. State the null and alternative hypotheses to be tested.
b. Compute the test statistic.
c. The null hypothesis is to be tested at the 1% level of significance. Determine the critical value from the table.
d. What do you conclude?

Free

Essay

Q 84Q 84

The following table shows the results of recent study regarding gender of individuals and their selected field of study.
We want to determine if the selected field of study is independent of gender.
a. Compute the test statistic.
b. Using the p-value approach at 90% confidence, test to see if the field of study is independent of gender.
c. Using the critical method approach at 90% confidence, test for the independence of major and gender.

Free

Essay

Q 85Q 85

Shown below is 3 x 2 contingency table with observed values from a sample of 1,500. At 95% confidence, test for independence of the row and column factors.
Column Factor

Free

Essay

Q 86Q 86

Shown below is 2 x 3 contingency table with observed values from a sample of 500. At 95% confidence using the critical value approach, test for independence of the row and column factors.
Column Factor

Free

Short Answer

Q 87Q 87

A sample of 150 individuals males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. Their incomes were categorized as follows.
The results of the survey are shown below.
We want to determine if yearly income is independent of gender.
a. Compute the test statistic.
b. Using the p-value approach, test to determine if yearly income is independent of gender.

Free

Essay

Q 88Q 88

A group of 2000 individuals from 3 different cities were asked whether they owned a foreign or a domestic car. The following contingency table shows the results of the survey.
At α = 0.05 using the p-value approach, test to determine if the type of car purchased is independent of the city in which the purchasers live.

Free

Essay

Q 89Q 89

Dr. Sherri Brock's diet pills are supposed to cause significant weight loss. The following table shows the results of a recent study where some individuals took the diet pills and some did not.
We want to see if losing weight is independent of taking the diet pills.
a. Compute the test statistic.
b. Using the p-value approach at 95% confidence, test to determine if weight loss is independent on taking the pill.
c. Use the critical method approach and test for independence.

Free

Essay

Q 90Q 90

Five hundred randomly selected automobile owners were questioned on the main reason they had purchased their current automobile. The results are given below.
a. State the null and alternative hypotheses for a contingency table test.
b. State the decision rule for the critical value approach. Let α = .01.
c. Calculate the χ2 test statistic.
d. Give your conclusion for this test.

Free

Essay

Q 91Q 91

A group of 500 individuals were asked to cast their votes regarding a particular issue of the Equal Rights Amendment. The following contingency table shows the results of the votes:
At α = .05 using the p-value approach, test to determine if the votes cast were independent of the sex of the individuals.

Free

Essay

Q 92Q 92

Two hundred fifty managers with degrees in business administration indicated their fields of concentration as shown below.
At α = .01 using the p-value approach, test to determine if the position in management is independent of the major of concentration.

Free

Essay

Q 93Q 93

The data below represents the fields of specialization for a randomly selected sample of undergraduate students. We want to determine whether there is a significant difference in the fields of specialization between regions of the country.
a. Determine the critical value of the chi-square χ2 for this test of independence.
b. Calculate the value of the test statistic.
c. What is the conclusion for this test? Let α = .05.

Free

Essay

Q 94Q 94

In a sample of 700 Republicans, 644 were opposed to the President's foreign policies. While in a sample of 600 Democrats, 528 were opposed to his policies. Develop a 95% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

Free

Short Answer

Q 95Q 95

Shoppers were asked where they do their regular grocery shopping. The table below shows their responses of the sampled shoppers. We are interested in determining if the proportions females in the three categories are different from each other.
a. Provide the null and the alternative hypotheses.
b. Determine the expected frequencies.
c. Compute the sample proportions.
d. Compute the critical values CVij).
e. Give your conclusions by providing numerical reasoning.

Free

Essay

Q 96Q 96

Prior to the start of the season, it was expected that audience proportions for the four major news networks would be CBS 18.6%, NBC 12.5%, ABC 28.9% and BBC 40%. A recent sample of homes yielded the following viewing audience data.
We want to determine whether or not the recent sample supports the expectations for the number of homes of the viewing audience of the four networks.
a. State the null and alternative hypotheses to be tested.
b. Compute the test statistic.
c. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test.
d. What do you conclude?

Free

Essay

Q 97Q 97

Prior to the start of the season, it was expected that audience proportions for the four major news networks would be CBS 28%, NBC 35%, ABC 22% and BBC 15%. A recent sample of homes yielded the following viewing audience data.
We want to determine whether or not the recent sample supports the expectations for the number of homes of the viewing audience of the four networks.
a. State the null and alternative hypotheses to be tested.
b. Compute the test statistic.
c. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test.
d. What do you conclude?

Free

Essay

Q 98Q 98

The results of a recent study regarding smoking and three types of illness are shown in the following table.
We are interested in determining whether or not illness is independent of smoking.
a. State the null and alternative hypotheses to be tested.
b. Show the contingency table of the expected frequencies and determine the test statistic.
c. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test
d. What do you conclude?

Free

Essay

Q 99Q 99

The results of a recent study regarding smoking and three types of illness are shown in the following table.
We are interested in determining whether or not illness is independent of smoking.
a. State the null and alternative hypotheses to be tested.
b. Show the contingency table of the expected frequencies and determine the test statistic.
c. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test.
d. What do you conclude?

Free

Essay