Question

The following data represent the level of happiness and level of health for a random sample of individuals from the General Social Survey. A researcher wants to determine if health and happiness level are related. Use the αα = 0.05 level of significance to test the claim.

Health

	Excellent	Good	Fair	Poor
Very Happy	271	261	82	20
Pretty Happy	247	567	231	53
Not Too Happy	33	103	92	36

*Source: General Social Survey

1) Determine the null and alternative hypotheses. Select the correct pair.

• Ho:Ho:Health and happiness are independent
  Ha:Ha: Health and happiness are dependent
• Ho:Ho: Health and happiness have the same distribution
  Ha:Ha: Health and happiness follow a different distribution

2) Determine the test Statistic. Round your answer to two decimals.

χ2 =

3) Determine the p-value. Round your answer to four decimals.

p-value =

4) Make a decision.

• Fail to reject the null hypothesis
• Reject the null hypothesis

5) Pick a conclusion.

• There is sufficient evidence to support the claim that health and happiness are related
• There is not sufficient evidence to support the claim that health and happiness are related

Answer 1

Excel:

Data --> Megastat --> Chi square --> Chi-square Contingency Table Test for Independence

Output:

1)

Ho:Health and happiness are independent
Ha: Health and happiness are dependent

2)

χ2 = 182.17

3)

P-value = 0.0000

4)

Reject the null hypothesis (since P-value = 0 <0.05=alpha)

5)

• There is sufficient evidence to support the claim that health and happiness are related