Question

You are doing a chi-square test with a 5 by 9 table of counts (that is, 5 rows and 9 columns).

What is the degrees of freedom?

Suppose you get ?^2 = 45.23. Calculate the p-value.

Suppose that you want to see if there is association between income level (high/medium/low) and gender.

a)Write the null hypothesis.

b)Use StatCrunch to calculate the test statistic (that is, the x^?2 value) and the p-value for this contingency table, which shows the income level for a random sample of adults cross classified by gender.

	Low	Middle	High	Total
Male	23	30	29	82
Female	26	28	20	74
Total	49	56	49	156

3.( YES / NO ) Based on the data in problem #2, there is a significant association between gender and income level (use significance level 0.05).

4.( YES / NO ) Based on the data in problem #2, there is a significant difference between the income levels for the two groups (males, females) (use significance level 0.01).

5.Use StatCrunch to find a 90% confidence interval to estimate the proportion of all females who have a high income level.

Answer 1

a)Write the null hypothesis.

Ans: Null hypothesis: There is no a significant association between row and column.

b)Use StatCrunch to calculate the test statistic (that is, the x 2 value) and the p-value for this

Ans: Suppose you get ?^2 = 45.23 and has  5 by 9 table of counts (that is, 5 rows and 9 columns). The estimated p-value for ?^2 = 45.23 at (5-1)(9-1)=32 degree of freedom is 0.0606.

2.

Null hypothesis: There is no a significant association between gender and income level

Alternative hypothesis: There is a significant association between gender and income level.

3)

		Observed (O)
	Low	Middle	High	Total
Male	23	30	29	82
Female	26	28	20	74
Total	49	56	49	156
		Expected ( E)
	Low	Middle	High
Male	25.7564103	29.4359	25.75641
Female	23.2435897	26.5641	23.24359
		(O-E)^2/E
	Low	Middle	High
Male	0.29498666	0.01081	0.408476
Female	0.32687711	0.077616	0.452636

Chi=square= Sum{(O-E)^2/E}= 1.5714

p-value =0.4558.

Ans: NO: Based on the data in problem #2, there is a significant association between gender and income level (use significance level 0.05).

4)

Ans: NO: Based on the data in problem #2, there is a significant difference between the income levels for the two groups (males, females) (use significance level 0.01).

5)