Question

Use the following contingency table to complete​ (a) and​ (b) below.

		A		B		C		Total
1		15		30		45		90
2		45		50		55		150
Total		60		80		100		240

a. Compute the expected frequencies for each cell.

		A		B		C
1
2
		​(Type integers or​ decimals.)

b. Compute χ2STAT. is it significant at α=0.005​?

Set up the null and alternative hypotheses to test. Choose the correct answer below.

1. H0​: πA= πB= πC

H1​:Not all πj are equal​ (where j=​A, ​B, C)

2. H0​: π1=π2

H1​: Not all jπj are equal​ (where j=​1, ​2)

3. H0​: Not all jπj are equal​ (where j=​A, ​B, C)

H1​: πA= πB= πC

4. H0​: Not all jπj are equal​ (where j=​1, ​2)

H1​: π1=π2

Compute χ2STAT.

χ2STAT=

​(Round to three decimal places as​ needed.)

Find the​ p-value.

​p-value=

​(Round to three decimal places as​ needed.)

Is χ2STAT significant at α=0.005​?

1. Yes​, because the​ p-value is greater than or equal to the level of significance.
2. Yes​, because the​ p-value is less than the level of significance.
3. No​, because the​ p-value is less than the level of significance.
4. No because the​ p-value is greater than or equal to the level of significance.

Answer 1

	A	B	C
1	22.5	30	37.5
2	37.5	50	62.5

χ2STAT= 6.4

P-VALUE = =CHISQ.DIST.RT(6.4,2) = 0.04076 = 0.041

p-value > alpha(0.005)

hence we fail to reject the null hypothesis

D) No because the​ p-value is greater than or equal to the level of significance.    is correct