STAT 121: Lesson 33

Use this information to answer the next nine questions. An exit poll was conducted in Utah County of the state of Utah on election day, November 2, 2004. Voters were randomly selected from the entire state and were questioned about which governor candidate they voted for and their religious affiliation. These results are summarized in this table. Referring to the table of observed counts and the table of expected counts, what is the chi-square test statistic component for the Huntsman-Catholic cell? (This is the cell in the upper-left corner of the table.)

25.722

Use this information to answer the next nine questions. An exit poll was conducted in Utah County of the state of Utah on election day, November 2, 2004. Voters were randomly selected from the entire state and were questioned about which governor candidate they voted for and their religious affiliation. These results are summarized in this table. What are the degrees of freedom for this chi-square test?

3

This scenario applies to this and the next six questions. A new medication has been developed to treat the common cold. This new medication was compared with a Vitamin C treatment and a placebo treatment in a clinical trial. 300 subjects who had colds were available for the study. The subjects were randomly allocated to the three treatments with 100 in each treatment group. At the end of the treatment period, each subject gave his/her opinion of the effectiveness of the treatment he/she received. Here are the results: What is the expected count for Medication who felt it "Helped"?

66.33

Suppose the p-value is 0.10. At the α = 0.05 level, what conclusion should be made?

Fail to reject H0. There is insufficient evidence that there is an association between treatment and opinion on effectiveness.

A small chi-square test statistic provides evidence against the null hypothesis.

False

Use this information to answer the next nine questions. An exit poll was conducted in Utah County of the state of Utah on election day, November 2, 2004. Voters were randomly selected from the entire state and were questioned about which governor candidate they voted for and their religious affiliation. These results are summarized in this table. The following table gives the row conditional distributions for each religious affiliation. On the basis of these conditional distributions, which religion is the only religion to have a higher proportion for Huntsman than for Matheson?

Latter-Day Saint

This scenario applies to this and the next six questions. A new medication has been developed to treat the common cold. This new medication was compared with a Vitamin C treatment and a placebo treatment in a clinical trial. 300 subjects who had colds were available for the study. The subjects were randomly allocated to the three treatments with 100 in each treatment group. At the end of the treatment period, each subject gave his/her opinion of the effectiveness of the treatment he/she received. Here are the results: Suppose the chi-square test statistic is 11.134327 with 3 degrees of freedom. Using the chi-square table, what is the p-value for this test?

0.01 < p-value < 0.02

This scenario applies to this and the next six questions. A new medication has been developed to treat the common cold. This new medication was compared with a Vitamin C treatment and a placebo treatment in a clinical trial. 300 subjects who had colds were available for the study. The subjects were randomly allocated to the three treatments with 100 in each treatment group. At the end of the treatment period, each subject gave his/her opinion of the effectiveness of the treatment he/she received. Here are the results: What are the appropriate degrees of freedom for this test? Hint: df = (r-1)(c-1)

2

This scenario applies to this and the next six questions. A new medication has been developed to treat the common cold. This new medication was compared with a Vitamin C treatment and a placebo treatment in a clinical trial. 300 subjects who had colds were available for the study. The subjects were randomly allocated to the three treatments with 100 in each treatment group. At the end of the treatment period, each subject gave his/her opinion of the effectiveness of the treatment he/she received. Here are the results: Assume the conditions for the test are met. What is the chi-square component for the Placebo subjects who answered "Didn't help"? Hint: calculate (Observed − Expected)2/Expected for that cell.

2.0608524

Use this information to answer the next nine questions. An exit poll was conducted in Utah County of the state of Utah on election day, November 2, 2004. Voters were randomly selected from the entire state and were questioned about which governor candidate they voted for and their religious affiliation. These results are summarized in this table. If there is no association between religious affiliation and candidate preference, how many Protestants do we "expect" to vote for Scott Matheson? In other words, what value should go in the cell containing "???" in the following table of expected counts:

92.63

Use this information to answer the next nine questions. An exit poll was conducted in Utah County of the state of Utah on election day, November 2, 2004. Voters were randomly selected from the entire state and were questioned about which governor candidate they voted for and their religious affiliation. These results are summarized in this table. What are the appropriate null and alternative hypotheses for this chi-square test?

H0: "Candidate preference and religious affiliation are not related." vs. Ha: "Candidate preference and religious affiliation are related."

This scenario applies to this and the next six questions. A new medication has been developed to treat the common cold. This new medication was compared with a Vitamin C treatment and a placebo treatment in a clinical trial. 300 subjects who had colds were available for the study. The subjects were randomly allocated to the three treatments with 100 in each treatment group. At the end of the treatment period, each subject gave his/her opinion of the effectiveness of the treatment he/she received. Here are the results: What are the appropriate hypotheses for this chi-square test?

Ho: "There is no association between Treatment and Opinion on effectiveness "Ha: "There is an association between Treatment and Opinion on effectiveness"

Use this information to answer the next nine questions. An exit poll was conducted in Utah County of the state of Utah on election day, November 2, 2004. Voters were randomly selected from the entire state and were questioned about which governor candidate they voted for and their religious affiliation. These results are summarized in this table. The p-value for the test as given by statistical software is less than 0.0001. On the basis of this p-value and the hypotheses given above, what should we conclude at α = 0.05?

Reject the null hypothesis and conclude that there is an association between candidate preference and religious affiliation

Use this information to answer the next nine questions. An exit poll was conducted in Utah County of the state of Utah on election day, November 2, 2004. Voters were randomly selected from the entire state and were questioned about which governor candidate they voted for and their religious affiliation. These results are summarized in this table. The location of each number in the following chi-square test statistic computation corresponds to the cell in the tables given above from which it is computed. On the basis of these cell contributions, which cell contributed most to the chi-square test statistic? Chi-Sq =25.725 + 37.874 +64.776 + 95.370 +5.101 + 7.510 +136.544 + 201.035 = 573.933

The "Matheson" / "Other" cell

If a chi-square test is significant (i.e., there is an association between the variables), we should look at the chi-square components as a follow-up analysis.

True

In a chi-square test, the "expected" counts are the values we expect if there is no association between the variables.

True

The "expected" counts for a chi-square test are the counts we expect if the null hypothesis is true.

True

This scenario applies to this and the next six questions. A new medication has been developed to treat the common cold. This new medication was compared with a Vitamin C treatment and a placebo treatment in a clinical trial. 300 subjects who had colds were available for the study. The subjects were randomly allocated to the three treatments with 100 in each treatment group. At the end of the treatment period, each subject gave his/her opinion of the effectiveness of the treatment he/she received. Here are the results: Refer to this table of expected counts. Is the sample size large enough to conduct a chi-square test?

Yes, all expected counts are greater than 5.

Use this information to answer the next nine questions. An exit poll was conducted in Utah County of the state of Utah on election day, November 2, 2004. Voters were randomly selected from the entire state and were questioned about which governor candidate they voted for and their religious affiliation. These results are summarized in this table. On the basis of the expected counts given in above table, is the sample size large enough for this chi-square test? Why?

Yes, because each cell has an expected count greater than 5.

Use this information to answer the next nine questions. An exit poll was conducted in Utah County of the state of Utah on election day, November 2, 2004. Voters were randomly selected from the entire state and were questioned about which governor candidate they voted for and their religious affiliation. These results are summarized in this table. Were the data appropriately collected for performing a chi-square test?

Yes, because voters were randomly selected.