Question 1

A die is rolled 180 times and the following data are obtained.Is the die fair?

Accepted Answer

A) 
 
: The die is not fair.
 
: The die is fair (all numbers occur with equal frequency).
Conclusion: Do not reject the null hypothesis.There is insufficient evidence to claim that the numbers on the die do not occur with equal frequency. 
B) 
 
: The die is not fair.
 
: The die is fair (all numbers occur with equal frequency).
Conclusion: Do not reject the null hypothesis.There is sufficient evidence to claim that the numbers on the die do not occur with equal frequency. 
C) 
 
: The die is fair (all numbers occur with equal frequency).
 
: The die is not fair.
Conclusion: Do not reject the null hypothesis.The data do not provide sufficient evidence to conclude that the die is loaded. 
D) 
 
: The die is fair (all numbers occur with equal frequency).
 
: The die is not fair.
Conclusion: Reject the null hypothesis.There is sufficient evidence to claim that the numbers on the die do not occur with equal frequency. 
E) 
 
: The die is not fair.
 
: The die is fair (all numbers occur with equal frequency).
Conclusion: Reject the null hypothesis.There is sufficient evidence to claim that the numbers on the die do not occur with equal frequency. 
A) 
 
: The die is not fair.
 
: The die is fair (all numbers occur with equal frequency).
Conclusion: Do not reject the null hypothesis.There is insufficient evidence to claim that the numbers on the die do not occur with equal frequency. 
B) 
 
: The die is not fair.
 
: The die is fair (all numbers occur with equal frequency).
Conclusion: Do not reject the null hypothesis.There is sufficient evidence to claim that the numbers on the die do not occur with equal frequency. 
C) 
 
: The die is fair (all numbers occur with equal frequency).
 
: The die is not fair.
Conclusion: Do not reject the null hypothesis.The data do not provide sufficient evidence to conclude that the die is loaded. 
D) 
 
: The die is fair (all numbers occur with equal frequency).
 
: The die is not fair.
Conclusion: Reject the null hypothesis.There is sufficient evidence to claim that the numbers on the die do not occur with equal frequency. 
E) 
 
: The die is not fair.
 
: The die is fair (all numbers occur with equal frequency).
Conclusion: Reject the null hypothesis.There is sufficient evidence to claim that the numbers on the die do not occur with equal frequency.

Question 2

When performing a chi-square goodness-of-fit test,how are the expected frequencies obtained?

Accepted Answer

The expected frequencies are the frequen

Question 3

Suppose that a chi-square goodness-of-fit test is to be performed.Is it true or false that the more closely the observed frequencies match the frequencies that would be expected if the null hypothesis were true,the larger the value of the test statistic   = Σ    ?

Accepted Answer

A) True 
 B)False

Question 4

The table below shows the age and favorite type of music of 668 randomly selected people.Use a 5% level of significance.  
 
= 12.954;P-value = 0.0115

Accepted Answer

A) Reject the null hypothesis and conclude that the age distribution is not the same for each type of music. 
B) Do not reject the null hypothesis and conclude that the age distribution is the same for each type of music. 
C) Do not reject the null hypothesis and conclude that the age distribution is not the same for each type of music. 
D) Reject the null hypothesis and conclude that the age distribution is uniform for each type of music. 
E) Reject the null hypothesis and conclude that the age distribution is the same for each type of music. 
A) Reject the null hypothesis and conclude that the age distribution is not the same for each type of music. 
B) Do not reject the null hypothesis and conclude that the age distribution is the same for each type of music. 
C) Do not reject the null hypothesis and conclude that the age distribution is not the same for each type of music. 
D) Reject the null hypothesis and conclude that the age distribution is uniform for each type of music. 
E) Reject the null hypothesis and conclude that the age distribution is the same for each type of music.

Question 5

Suppose that you wish to perform a chi-square test of independence.The two variables under consideration are sex and blood type.Is it true or false that if the two variables are not associated,we would expect that the proportion of women in the sample with a given blood type would be roughly equal to the proportion of men in the sample with the same blood type?

Accepted Answer

A) True 
 B)False

Question 6

The sample data below was tested to determine whether car colour is related to the likelihood of being in an accident.   
Test statistic: χ2 =34.38
P-value = 3.42 ×

Accepted Answer

We reject the null hypothesis that car c

Question 7

A researcher wishes to test the effectiveness of a flu vaccination.150 people are vaccinated,180 people are vaccinated with a placebo,and 100 people are not vaccinated.The number in each group who later caught the flu was recorded.The results are shown below.   
Are the proportions of people catching the flu the same in all three groups? Use a 1% level of significance.

Accepted Answer

H₀: The proportion of people catching the

Question 8

The table below shows the age and favorite type of music of 668 randomly selected people.   
Are age and preferred music type are associated? Use a 5% level of significance.

Accepted Answer

H₀: Age and preferred music type are inde

Question 9

A researcher records for each of 500 randomly selected towns,the number of churches in the town and the number of homicides in the town in the past ten years.The towns range in size from a population of 1000 to a population of 1,000,000.He then performs a chi-square test of independence for these two variables.Would you expect that he would find association between the two variables? If so,should he conclude that a causal relationship exists? Explain your thinking.

Accepted Answer

The researcher will probably find associ

Question 10

Suspecting that a die may be unfair,you want to investigate.To check,you roll it 54 times,recording the number of times each face appears.  
How many degrees of freedom are there?

Accepted Answer

A) 12 
B) 6 
C) 3 
D) 5 
E) 16 
A) 12 
B) 6 
C) 3 
D) 5 
E) 16

Question 11

A car insurance company performed a study to determine whether an association exists between age and the frequency of car accidents.They obtained the following sample data.Use a 5% level of significance.  
 
= 9.13;P-value = 0.0579

Accepted Answer

A) Do not reject the null hypothesis.One can conclude that there is a relationship between age and number of accidents. 
B) Do not reject the null hypothesis.The data do not provide sufficient evidence to conclude that the number of accidents is distributed uniformly for each age group. 
C) Reject the null hypothesis.One cannot conclude that there is a relationship between age and number of accidents. 
D) Do not reject the null hypothesis.The data do not provide sufficient evidence to conclude that there is an association between age and frequency of car accidents. 
E) Reject the null hypothesis.One can conclude that there is a relationship between age and number of accidents. 
A) Do not reject the null hypothesis.One can conclude that there is a relationship between age and number of accidents. 
B) Do not reject the null hypothesis.The data do not provide sufficient evidence to conclude that the number of accidents is distributed uniformly for each age group. 
C) Reject the null hypothesis.One cannot conclude that there is a relationship between age and number of accidents. 
D) Do not reject the null hypothesis.The data do not provide sufficient evidence to conclude that there is an association between age and frequency of car accidents. 
E) Reject the null hypothesis.One can conclude that there is a relationship between age and number of accidents.

Question 12

A company says that each bag of their candy pieces contains 15% chocolate,27% butterscotch,10% caramel,7% peanut butter,and the rest toffee.You can buy a bag and separate the various kinds of candies.Upon weighing them,you find there are 30 grams of chocolate,48 grams of butterscotch,57 grams of caramel,63 grams of peanut butter and 90 grams of toffee.You wonder whether your bag is significantly different from what the company advertises.

Accepted Answer

A) Yes 
B) No,because the expected values are unclear. 
C) No,because it is not possible to find the residuals. 
D) No,because the data are quantitative. 
E) No,because the observed counts are too close to the expected counts. 
A) Yes 
B) No,because the expected values are unclear. 
C) No,because it is not possible to find the residuals. 
D) No,because the data are quantitative. 
E) No,because the observed counts are too close to the expected counts.

Question 13

Responses to a survey question are broken down according to gender and the sample results are given below.Are the response and gender are independent?

Accepted Answer

H₀: Gender and response are independent.

Question 14

The two-way table summarizes data from the human resource department at a university:
New Hires  
What is the probability (rounded to two decimal places)that a randomly selected new hire is a tenure-track woman?

Accepted Answer

A) 0 
B) 0.21 
C) 0.43 
D) 0.15 
E) 0.50 
A) 0 
B) 0.21 
C) 0.43 
D) 0.15 
E) 0.50

Question 15

A candy company claims that its bags of mixed suckers are 20% strawberry,30% cherry,15% apple,10% lemon,and 25% grape.A bag was purchased,and the number of each type of flavour was recorded in the chart below.

Accepted Answer

A) 
 
: The distribution of flavours is not the same as the distribution claimed by the company.
 
: The distribution of flavours is the same as the distribution claimed by the company. 
B) 
 
: The distribution of flavours is the same as the distribution claimed by the company.
 
: The distribution of flavours is not the same as the distribution claimed by the company. 
C) 
 
: The distribution of flavours is not uniform.
 
: The distribution of flavours is uniform. 
D) 
 
: The distribution of flavours is uniform.
 
: The distribution of flavours is not uniform. 
E) 
 
: The flavours and counts are independent.
 
: The flavours and counts are not independent. 
A) 
 
: The distribution of flavours is not the same as the distribution claimed by the company.
 
: The distribution of flavours is the same as the distribution claimed by the company. 
B) 
 
: The distribution of flavours is the same as the distribution claimed by the company.
 
: The distribution of flavours is not the same as the distribution claimed by the company. 
C) 
 
: The distribution of flavours is not uniform.
 
: The distribution of flavours is uniform. 
D) 
 
: The distribution of flavours is uniform.
 
: The distribution of flavours is not uniform. 
E) 
 
: The flavours and counts are independent.
 
: The flavours and counts are not independent.

Question 16

Tests for adverse reactions to a new drug yielded the results given in the table.Use a 10% level of significance.  
 
= 1.798;P-value = 0.1799
The data will be analyzed to determine if there is sufficient evidence to conclude that an association exists between the treatment (drug or placebo)and the reaction (whether or not headaches were experienced).

Accepted Answer

A) Do not reject the null hypothesis.Report that there is insufficient evidence to conclude that the distribution of headaches is uniform for the drug and placebo. 
B) Reject the null hypothesis.Report that there is sufficient evidence to conclude that treatment and reaction are dependent. 
C) Reject the null hypothesis.Report that there is insufficient evidence to conclude that treatment and reaction are dependent. 
D) Do not reject the null hypothesis.Report that there is sufficient evidence to conclude that treatment and reaction are dependent. 
E) Do not reject the null hypothesis.Report that there is insufficient evidence to conclude that treatment and reaction are dependent. 
A) Do not reject the null hypothesis.Report that there is insufficient evidence to conclude that the distribution of headaches is uniform for the drug and placebo. 
B) Reject the null hypothesis.Report that there is sufficient evidence to conclude that treatment and reaction are dependent. 
C) Reject the null hypothesis.Report that there is insufficient evidence to conclude that treatment and reaction are dependent. 
D) Do not reject the null hypothesis.Report that there is sufficient evidence to conclude that treatment and reaction are dependent. 
E) Do not reject the null hypothesis.Report that there is insufficient evidence to conclude that treatment and reaction are dependent.

Question 17

A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges.She randomly selects 100 students from each college and records the number that smoke.The results are shown below.   
Are the proportions of students smoking the same for all four colleges? Use a 1% level of significance.

Accepted Answer

H₀: The proportion of students smoking is

Question 18

In studying the occurrence of genetic characteristics,the following sample data were obtained.Do the characteristics occur with the same frequency? Use a 10% level of significance.  
Χ2 = 8.263;P-value = 0.1423

Accepted Answer

A) Reject the null hypothesis.There is sufficient evidence to warrant rejection of the claim that the characteristics occur with the same frequency. 
B) Fail to reject the null hypothesis.There is not sufficient evidence to warrant rejection of the claim that the characteristics occur with the same frequency. 
C) Fail to reject the null hypothesis.There is not sufficient evidence to warrant rejection of the claim that the characteristics are independent. 
D) Fail to reject the null hypothesis.There is sufficient evidence to warrant rejection of the claim that the characteristics occur with the same frequency. 
E) Reject the null hypothesis.There is not sufficient evidence to warrant rejection of the claim that the characteristics occur with the same frequency. 
A) Reject the null hypothesis.There is sufficient evidence to warrant rejection of the claim that the characteristics occur with the same frequency. 
B) Fail to reject the null hypothesis.There is not sufficient evidence to warrant rejection of the claim that the characteristics occur with the same frequency. 
C) Fail to reject the null hypothesis.There is not sufficient evidence to warrant rejection of the claim that the characteristics are independent. 
D) Fail to reject the null hypothesis.There is sufficient evidence to warrant rejection of the claim that the characteristics occur with the same frequency. 
E) Reject the null hypothesis.There is not sufficient evidence to warrant rejection of the claim that the characteristics occur with the same frequency.

Exam 25: Comparing Counts

A die is rolled 180 times and the following data are obtained.Is the die fair?

When performing a chi-square goodness-of-fit test,how are the expected frequencies obtained?

Suppose that a chi-square goodness-of-fit test is to be performed.Is it true or false that the more closely the observed frequencies match the frequencies that would be expected if the null hypothesis were true,the larger the value of the test statistic = Σ ?

The table below shows the age and favorite type of music of 668 randomly selected people.Use a 5% level of significance. = 12.954;P-value = 0.0115

The sample data below was tested to determine whether car colour is related to the likelihood of being in an accident. Test statistic: χ2 =34.38 P-value = 3.42 ×

The table below shows the age and favorite type of music of 668 randomly selected people. Are age and preferred music type are associated? Use a 5% level of significance.

Suspecting that a die may be unfair,you want to investigate.To check,you roll it 54 times,recording the number of times each face appears. How many degrees of freedom are there?

A car insurance company performed a study to determine whether an association exists between age and the frequency of car accidents.They obtained the following sample data.Use a 5% level of significance. = 9.13;P-value = 0.0579

Responses to a survey question are broken down according to gender and the sample results are given below.Are the response and gender are independent?

The two-way table summarizes data from the human resource department at a university: New Hires What is the probability (rounded to two decimal places)that a randomly selected new hire is a tenure-track woman?

A candy company claims that its bags of mixed suckers are 20% strawberry,30% cherry,15% apple,10% lemon,and 25% grape.A bag was purchased,and the number of each type of flavour was recorded in the chart below.

In studying the occurrence of genetic characteristics,the following sample data were obtained.Do the characteristics occur with the same frequency? Use a 10% level of significance. Χ2 = 8.263;P-value = 0.1423

Data

Displaying and Describing Categorical Data

Displaying and Summarizing Quantitative Data

Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Linear Regression

Regression Wisdom

Re-Expressing Data: Get It Straight

Understanding Randomness

Sample Surveys

Experiments and Observational Surveys

From Randomness to Probability

Probability Rules

Random Variables

Probability Models

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Comparing Means

Paired Samples and Blocks

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Multiple Regression Wisdom

Rank-Based Nonparametric Tests

The Bootstrap

Filters

The sample data below was tested to determine whether car colour is related to the likelihood of being in an accident. Test statistic: χ² =34.38 P-value = 3.42 ×

In studying the occurrence of genetic characteristics,the following sample data were obtained.Do the characteristics occur with the same frequency? Use a 10% level of significance. Χ² = 8.263;P-value = 0.1423