Question 1

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

The p-value is less than the significance level of 0.05, which means there is sufficient evidence to reject the null hypothesis. Therefore, we can conclude that the age distribution is not the same for each type of music.

Question 2

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. Test statistic: χ² = 17.832 P-value = 0.0004763

Accepted Answer

The answer of A researcher wishes to test whether the...

Question 3

Research is conducted regarding the average age at retirement for four career groups.To test whether there is a relationship between age of retirement and career in these groups,700 employees,recently retired,are randomly selected.The resulting data are displayed in the contingency table below. 
How many degrees of freedom are there for the chi-square test statistic?

Accepted Answer

To calculate degrees of freedom for a chi-square test, we use the formula: (number of rows - 1) x (number of columns - 1). In this case, there are 4 rows and 3 columns, so degrees of freedom = (4-1) x (3-1) = 9. Therefore, the answer is B, 9.

Question 4

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

Accepted Answer

The answer of When performing a chi-square goodness-of-fit test,how are...

Question 5

In order to test a claim about the effectiveness of a flu vaccine,150 people were vaccinated,180 people were vaccinated with a placebo,and 100 people were not vaccinated.The number in each group who later caught the flu was recorded.The researcher wishes to test the claim that the proportion of people who catch the flu is the same for all three groups.The results are shown below. Test statistic: χ² = 14.965 P-value = 0.0005627

Accepted Answer

The answer of In order to test a claim about...

Question 6

What is the null hypothesis for the chi-square test of independence? What assumptions are required for this test?

Accepted Answer

The answer of What is the null hypothesis for the...

Question 7

Describe the null hypothesis for the test of independence.List the assumptions for the χ² test of independence.What is the major difference between the assumptions for this test and the assumptions for the previous tests we have studied?

Accepted Answer

The answer of Describe the null hypothesis for the test...

Question 8

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

The answer of Suppose that a chi-square goodness-of-fit test is...

Question 9

Explain why a chi-square goodness-of-fit test is always right-tailed.

Accepted Answer

The answer of Explain why a chi-square goodness-of-fit test is...

Question 10

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 answer of A researcher records for each of 500...

Question 11

Describe a goodness-of-fit test.What assumptions are made when using a goodness-of-fit test?

Accepted Answer

The answer of Describe a goodness-of-fit test.What assumptions are made...

Question 12

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

The p-value of 0.1423 is greater than the significance level of 0.10. Therefore, we fail to reject the null hypothesis, which states that the characteristics occur with the same frequency. There is not sufficient evidence to support the claim that the characteristics occur with different frequencies.

Question 13

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

If the variables are not associated, then the distribution of one variable should not depend on the other. Therefore, we would expect the proportion of women with a particular blood type to be roughly equal to the proportion of men with the same blood type.

Question 14

A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies.He compiled the following data. Test statistic: χ² = 28.308 P-value = 0.0000108

Accepted Answer

The answer of A company manager wishes to test a...

Question 15

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

The answer of The sample data below was tested to...

Question 16

160 students who were majoring in either math or English were asked a test question,and the researcher recorded whether they answered the question correctly.The sample results are given below.

= 6.502;P-value = 0.011
Are the response and major independent? Use a 5% level of significance.

Accepted Answer

The null hypothesis in this case is that the response (correct or incorrect) is independent of the major. Since the P-value is less than the significance level of 0.05, we reject the null hypothesis. This means that we have evidence to conclude that the response is dependent on major, hence choice D is the correct answer.

Question 17

A die is rolled 180 times and the following data are obtained. 
A chi-square test was conducted to determine whether or not the die is loaded (i.e. ,that the six numbers are not equally likely).Use a 5% level of significance. 
= 11.8;P-value = 0.03763

Accepted Answer

The chi-square test results in a test statistic of 11.8 and a p-value of 0.03763. Since the p-value is less than the level of significance of 5%, we reject the null hypothesis. Therefore, we can conclude that the die is loaded and that the six numbers are not equally likely. Choice letter A is the correct choice.

Question 18

When performing a chi-square goodness-of-fit test,why do large values of the test statistic suggest that the variable does not have the distribution stated in the null hypothesis? Refer to the formula for the test statistic in your explanation.

Accepted Answer

The answer of When performing a chi-square goodness-of-fit test,why do...

Quiz 25: Comparing Counts

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

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. Test statistic: χ² = 17.832 P-value = 0.0004763

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

What is the null hypothesis for the chi-square test of independence? What assumptions are required for this test?

Describe the null hypothesis for the test of independence.List the assumptions for the χ² test of independence.What is the major difference between the assumptions for this test and the assumptions for the previous tests we have studied?

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 ?

Explain why a chi-square goodness-of-fit test is always right-tailed.

Describe a goodness-of-fit test.What assumptions are made when using a goodness-of-fit test?

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

A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies.He compiled the following data. Test statistic: χ² = 28.308 P-value = 0.0000108

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 ×

160 students who were majoring in either math or English were asked a test question,and the researcher recorded whether they answered the question correctly.The sample results are given below. = 6.502;P-value = 0.011 Are the response and major independent? Use a 5% level of significance.

A die is rolled 180 times and the following data are obtained. A chi-square test was conducted to determine whether or not the die is loaded (i.e. ,that the six numbers are not equally likely) .Use a 5% level of significance. = 11.8;P-value = 0.03763

When performing a chi-square goodness-of-fit test,why do large values of the test statistic suggest that the variable does not have the distribution stated in the null hypothesis? Refer to the formula for the test statistic in your explanation.

Quiz 25: Comparing Counts

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

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. Test statistic: χ2 = 17.832 P-value = 0.0004763

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

What is the null hypothesis for the chi-square test of independence? What assumptions are required for this test?

Describe the null hypothesis for the test of independence.List the assumptions for the χ2 test of independence.What is the major difference between the assumptions for this test and the assumptions for the previous tests we have studied?

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 ?

Explain why a chi-square goodness-of-fit test is always right-tailed.

Describe a goodness-of-fit test.What assumptions are made when using a goodness-of-fit test?

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

A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies.He compiled the following data. Test statistic: χ2 = 28.308 P-value = 0.0000108

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 ×

160 students who were majoring in either math or English were asked a test question,and the researcher recorded whether they answered the question correctly.The sample results are given below. = 6.502;P-value = 0.011 Are the response and major independent? Use a 5% level of significance.

A die is rolled 180 times and the following data are obtained. A chi-square test was conducted to determine whether or not the die is loaded (i.e. ,that the six numbers are not equally likely) .Use a 5% level of significance. = 11.8;P-value = 0.03763

When performing a chi-square goodness-of-fit test,why do large values of the test statistic suggest that the variable does not have the distribution stated in the null hypothesis? Refer to the formula for the test statistic in your explanation.

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. Test statistic: χ² = 17.832 P-value = 0.0004763

Describe the null hypothesis for the test of independence.List the assumptions for the χ² test of independence.What is the major difference between the assumptions for this test and the assumptions for the previous tests we have studied?

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

A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies.He compiled the following data. Test statistic: χ² = 28.308 P-value = 0.0000108

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 ×