# What are mean & standard deviation of test statistic?

Questions 14 through 19 are based on the following scenario.

The following data are the results of a study where subjects were classified according to the amount they snored (as reported by their spouses) and whether they had a history of heart disease. The researchers were interested in the question of whether snoring and heart disease are related.

HEARTDIS Heart Disease? by SNORE Snoring Status

SNORE

Count | occasion snores snores

|nonsnore snore nearly every Row

| 1 | 2 | 3 | 4 | Total

HEARTDIS ——–+——–+——–+——–+——–+

1 | 24 | 35 | 21 | 30 | 110

yes | | | | | 4.4

+——–+——–+——–+——–+

2 | 1355 | 603 | 192 | 224 | 2374

no | | | | | 95.6

+——–+——–+——–+——–+

Column 1379 638 213 254 2484

Total 55.5 25.7 8.6 10.2 100.0

Chi-Square Value DF Significance

——————– ——– —- ————

Pearson 72.78206 3 .00000

Likelihood Ratio 65.90448 3 .00000

14.What is the appropriate null hypothesis of interest here?

15.Using a 5% significance level, give the test statistic value, the p-value, your decision, and corresponding conclusion for testing the null hypothesis in problem 14.

16.When the null hypothesis is true, what are the mean and standard deviation of the test statistic?

17.The data was collected from both females and males. The output for the male subpopulation is provided next. Does the conclusion in problem 15 hold true for the male subpopulation at the 5% significance level?

HEARTDIS Heart Disease? by SNORE Snoring Status

SNORE

Count | occasion snores snores

|nonsnore snore nearly every Row

| 1 | 2 | 3 | 4 | Total

HEARTDIS ——–+——–+——–+——–+——–+

1 | 15 | 21 | 15 | 19 | 70

yes | | | | | 9.1

+——–+——–+——–+——–+

2 | 220 | 200 | 120 | 158 | 698

no | | | | | 90.9

+——–+——–+——–+——–+

Column 235 221 135 177 768

Total 30.6 28.8 17.6 23.0 100.0

Chi-Square Value DF Significance

——————– ——– —- ————

Pearson 3.36714 3 .33841

Likelihood Ratio 3.52628 3 .31737

18.The output for the female subpopulation is provided next. Does the conclusion in problem 15 hold true for the female subpopulation at the 5% significance level?

HEARTDIS Heart Disease? by SNORE Snoring Status

SNORE

Count | occasion snores snores

|nonsnore snore nearly every Row

| 1 | 2 | 3 | 4 | Total

HEARTDIS ——–+——–+——–+——–+——–+

1 | 9 | 14 | 6 | 11 | 40

yes | | | | | 2.3

+——–+——–+——–+——–+

2 | 1135 | 403 | 72 | 66 | 1676

no | | | | | 97.7

+——–+——–+——–+——–+

Column 1144 417 78 77 1716

Total 66.7 24.3 4.5 4.5 100.0

Chi-Square Value DF Significance

——————– ——– —- ————

Pearson 72.09638 3 .00000

Likelihood Ratio 46.60901 3 .00000

19.Briefly explain why the aggregated results (aggregated across gender) are misleading.

Questions 20 through 25 are based on the following scenario.

A clothing company wishes to find out more about people’s favorite season for purchasing clothes, so they can adjust their designs and production levels. A survey is conducted among 500 randomly selected people. They are asked what their favorite season is and the following results are obtained.

Winter

Spring

Summer

Fall

Total

37

143

218

102

500

20.What type of chi-square test should be conducted?

21.Industry standards have always been set at the following: 10% of the people have winter as their favorite season, 30% have spring as their favorite season, 40% the summer, and 20% the fall. What is the null hypothesis for the test of question 20?

22.What test statistic is calculated to perform the test of question 20? What is its distribution under the null hypothesis?

23.How many people would the clothing company expect to see in each of the 4 categories?

24.What is the value of the test statistic mentioned in question 22?

25.Do the observed counts support the industry standards? Perform the test at a 10% significance level.