Question

Use this information to answer the following questions:  We have data here from a sample of middle aged people. The columns represent the level of sports they played while the rows represent whether they have developed arthritis later in life.

Observed		College	High school	Did not play
	Arthritis	10	9	24
	No arthritis	61	206	548

Run the appropriate test to see if playing sports has an effect on arthritis late in life.

What are your hypotheses?

Ho: Data fits the hypothesized distribution; Ho: Data does not fit the hypothesized distribution

Ho: No association between the variables; Ha: There is an association between the variable

Ho: All groups are the same; Ha: All groups are different

Run the appropriate test to see if playing sports has an effect on arthritis late in life.

What is your resulting test statistic?

What is the appropriate degrees of freedom?

What is your best estimate of the p-val?

What decision should you make?

Answer 1

Ans:

Hypothesis statements:

Ho: No association between the variables;

Ha: There is an association between the variable

Chi square test for independence:

	Observed(fo)
	college	high school	did not play	Total
Arthritis	10	9	24	43
No arthritis	61	206	548	815
Total	71	215	572	858
	Expected(fe)
	college	high school	did not play	Total
Arthritis	3.56	10.78	28.67	43
No arthritis	67.44	204.22	543.33	815
Total	71	215	572	858
	Chi square=(fo-fe)^2/fe
	college	high school	did not play	Total
Arthritis	11.662	0.292	0.760	12.714
No arthritis	0.615	0.015	0.040	0.671
Total	12.277	0.308	0.800	13.385

Test statistic:

Chi square=13.385

df=(2-1)*(3-1)=2

p-value=CHIDIST(13.385,2)=0.0012

Reject the null hypothesis.