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Posted: January 25th, 2016

. Conduct a chi-square test on these data. Report the hypotheses, test statistic, and p-value. Summarize your conclusion

Many songs associate Mondays with having the blues, but are people really more likely to commit suicide on Mondays? A recent study (Kposowa et al., 2009) analyzed data on suicides in the United States between the years 2000 and 2004. They classified each suicide according to the day of the week on which it occurred. Their data produced the following sample percentages:

A news article that described this study did not report the sample size. Suppose for now that the sample size was 252. The computer output below presents results of a chi-square goodness-of-fit test of equal proportions:

a. Explain how the expected counts were calculated.

Seven is divided by the sample size.
The sample size is divided by percentage of suicides for each day.
The percentage of suicides for each day is divided by the sample size.
The sample size is divided by seven.
The percentage of suicides for each day is multiplied by the sample size.

b. Choose how the chi-square contribution for Monday was calculated.

c. Interpret what the p-value means in this context.

The p-value is the probability of obtaining sample counts that result in a small chi-square test statistic, assuming that the probability of a suicide on each of the seven weekdays is not the same.
The p-value is the probability of obtaining sample counts that result in a large chi-square test statistic, assuming that the probability of a suicide on each of the seven weekdays is the same.
The p-value is the probability of obtaining sample counts that result in a small chi-square test statistic, assuming that the probability of a suicide on each of the seven weekdays is the same.
The p-value is the probability of obtaining sample counts that result in a large chi-square test statistic, assuming that the probability of a suicide on each of the seven weekdays is not the same.

d. Summarize the conclusion that you would draw from this p-value.

You have no statistical evidence that the probability of a suicide occurring on any of the seven weekdays is not the same.
You have weak statistical evidence that the probability of a suicide occurring on any of the seven weekdays is not the same.
You have strong statistical evidence that the probability of a suicide occurring on any of the seven weekdays is not the same.

e. Which day appears to be especially likely for suicides?

Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday

f. If the sample size were larger, and the sample percentages stayed the same, how would the p-value change?

The p-value would increase.
The p-value would decrease.
The p-value would stay the same.

Unit 6, Topic 25, Exercise 25-22

Preventing Breast Cancer

The Study of Tamoxifen and Raloxifene (STAR) enrolled more than 19,000 postmenopausal women who were at increased risk for breast cancer. Women were randomly assigned to receive one of the drugs (tamoxifen or raloxifene) daily for five years. During the course of the study, researchers kept track of which women developed invasive breast cancer and which women did not. The initial results released in April 2006 revealed that 163 of 9726 women in the tamoxifen group had developed invasive breast cancer, compared to 167 of the 9745 women in the raloxifene group.

a. Organize this information into a 2 times 2 table.

Tamoxifen Raloxifene Total
Breast Cancer
No Breast Cancer
Total
b. Calculate the expected counts, under the null hypothesis that the population proportions of women who would develop breast cancer are the same with both treatments.

Round your answers to three decimal places.

Tamoxifen Raloxifene
Breast Cancer
No Breast Cancer
c. Conduct a chi-square test on these data. Report the hypotheses, test statistic, and p-value. Summarize your conclusion.

Round the test statistic to three decimal places. Use the chi-square distribution table to find a range for the p-value. If there is no lower limit on the p-value, enter 0 for the lower limit. If there is no upper limit on the p-value, enter 1 for the upper limit.

Upper H Subscript 0 Baseline colon pi Subscript Tamoxifen
 

≠
=
>
pi Subscript Raloxifene

Upper H Subscript a Baseline colon pi Subscript Tamoxifen
 

≠
=
>
pi Subscript Raloxifene

The test statistic is chi Superscript 2 Baseline equals.

less-than p-valueless-than

We 
 
reject
do not reject
 Upper H Subscript 0.

d. Suppose someone else decided to perform a two-sample z-test and found that z equals negative 0.2 and p-valueequals 0.838 Comment on how this compares to the test statistic and p-value you just calculated.

The test statistic of the chi-square test is roughly 
 
the square root of
the square of
double
half of
the same as
 the test statistic of the two-sample z-test.

Attachments:
application/pdf iconexercise_24-25.pdf
application/pdf iconexercise_25-22.pdf

Many songs associate Mondays with having the blues, but are people really more likely to commit suicide on Mondays? A recent study (Kposowa et al., 2009) analyzed data on suicides in the United States between the years 2000 and 2004. They classified each suicide according to the day of the week on which it occurred. Their data produced the following sample percentages:

A news article that described this study did not report the sample size. Suppose for now that the sample size was 252. The computer output below presents results of a chi-square goodness-of-fit test of equal proportions:

a. Explain how the expected counts were calculated.

Seven is divided by the sample size.
The sample size is divided by percentage of suicides for each day.
The percentage of suicides for each day is divided by the sample size.
The sample size is divided by seven.
The percentage of suicides for each day is multiplied by the sample size.

b. Choose how the chi-square contribution for Monday was calculated.

c. Interpret what the p-value means in this context.

The p-value is the probability of obtaining sample counts that result in a small chi-square test statistic, assuming that the probability of a suicide on each of the seven weekdays is not the same.
The p-value is the probability of obtaining sample counts that result in a large chi-square test statistic, assuming that the probability of a suicide on each of the seven weekdays is the same.
The p-value is the probability of obtaining sample counts that result in a small chi-square test statistic, assuming that the probability of a suicide on each of the seven weekdays is the same.
The p-value is the probability of obtaining sample counts that result in a large chi-square test statistic, assuming that the probability of a suicide on each of the seven weekdays is not the same.

d. Summarize the conclusion that you would draw from this p-value.

You have no statistical evidence that the probability of a suicide occurring on any of the seven weekdays is not the same.
You have weak statistical evidence that the probability of a suicide occurring on any of the seven weekdays is not the same.
You have strong statistical evidence that the probability of a suicide occurring on any of the seven weekdays is not the same.

e. Which day appears to be especially likely for suicides?

Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday

f. If the sample size were larger, and the sample percentages stayed the same, how would the p-value change?

The p-value would increase.
The p-value would decrease.
The p-value would stay the same.

Unit 6, Topic 25, Exercise 25-22

Preventing Breast Cancer

The Study of Tamoxifen and Raloxifene (STAR) enrolled more than 19,000 postmenopausal women who were at increased risk for breast cancer. Women were randomly assigned to receive one of the drugs (tamoxifen or raloxifene) daily for five years. During the course of the study, researchers kept track of which women developed invasive breast cancer and which women did not. The initial results released in April 2006 revealed that 163 of 9726 women in the tamoxifen group had developed invasive breast cancer, compared to 167 of the 9745 women in the raloxifene group.

a. Organize this information into a 2 times 2 table.

Tamoxifen Raloxifene Total
Breast Cancer
No Breast Cancer
Total
b. Calculate the expected counts, under the null hypothesis that the population proportions of women who would develop breast cancer are the same with both treatments.

Round your answers to three decimal places.

Tamoxifen Raloxifene
Breast Cancer
No Breast Cancer
c. Conduct a chi-square test on these data. Report the hypotheses, test statistic, and p-value. Summarize your conclusion.

Round the test statistic to three decimal places. Use the chi-square distribution table to find a range for the p-value. If there is no lower limit on the p-value, enter 0 for the lower limit. If there is no upper limit on the p-value, enter 1 for the upper limit.

Upper H Subscript 0 Baseline colon pi Subscript Tamoxifen
 

≠
=
>
pi Subscript Raloxifene

Upper H Subscript a Baseline colon pi Subscript Tamoxifen
 

≠
=
>
pi Subscript Raloxifene

The test statistic is chi Superscript 2 Baseline equals.

less-than p-valueless-than

We 
 
reject
do not reject
 Upper H Subscript 0.

d. Suppose someone else decided to perform a two-sample z-test and found that z equals negative 0.2 and p-valueequals 0.838 Comment on how this compares to the test statistic and p-value you just calculated.

The test statistic of the chi-square test is roughly 
 
the square root of
the square of
double
half of
the same as
 the test statistic of the two-sample z-test.

Attachments:
application/pdf iconexercise_24-25.pdf
application/pdf iconexercise_25-22.pdf

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