Question

In: Math

Use the following contingency table to complete​ (a) and​ (b) below. A B C Total 1...

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)

  1. H0​: π1=π2

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

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

H1​: πA= πB= πC

  1. 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.

Solutions

Expert Solution

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


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