Use the following information to calculate your answers to q

Use the following information to calculate your answers to questions 1 through 12.

The table below shows the results of a study on smoking and three illnesses. We are interested in determining if the proportions of smokers in the three categories are different from each other.

p₁ = proportions of smokers with emphysema

p₂ = proportions of smokers with heart problem

p₃ = proportions of smokers with cancer

Question 1

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Which of the following represents the null and alternative hypotheses in this case?

Select one:

a. H_o: p₁ = p₂ = p₃                              H_a: Not all population proportions are equal

b. H_o: p₁ = p₃                                      H_a: p₃ = p₂

c. H_o: p₁ = p₂                                      H_a: p₂ = p₃

d. H_o: p₁ = p₂ = p₃ = p_total                 H_a: Not all population proportions are equal

Question 2

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The expected frequency of non-smokers with heart problem is

Select one:

a. 318

b. 96

c. 212

d. 144

e. 0.60

Question 3

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The expected frequency of smokers with cancer is

Select one:

a. 96

b. 212

c. 144

d. 0.40

e. 318

Question 4

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The expected frequency of non-smokers with emphysema is

Select one:

a. 318

b. 123

c. 96

d. 82

e. 0.40

Question 5

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The expected frequency of smokers with emphysema is

Select one:

a. 82

b. 0.40

c. 96

d. 212

e. 123

Question 6

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The chi-square value is

Select one:

a. 27.12

b. 1.52

c. 12.66

d. 1.01

e. 5.90

Question 7

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With = 0.1, the critical X² value is

Select one:

a. 10.645

b. 4.605

c. 6.251

d. 2.706

e. 9.236

Question 8

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The conclusion is

Select one:

a. reject H_o since X² is less than critical X².

b. accept H_o since X² is greater than critical X².

c. No conclusion can be drawn.

d. reject H_o since X² is greater than critical X².

e. accept H_o since X² is less than critical X².

Question 9

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P₁ – P₂ is

Select one:

a. 0.14

b. 0.097

c. 0.12

d. 5

e. –21

Question 10

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P₂ – P₃ is

Select one:

a. 0.097

b. 0.017

c. 5

d. 0.082

e. 0.14

Question 11

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CV₂₃ is

Select one:

a. 0.017

b. 0.097

c. 5

d. 0.082

e. 0.14

Question 12

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Using = 0.1, the conclusion of the pairwise comparison is

Select one:

a. emphysema vs heart problem & heart problem vs cancer are significant.

b. emphysema vs cancer & heart problem vs cancer are significant.

c. All pairwise comparisons are significant.

d. emphysema vs heart problem & emphysema vs cancer are significant.

e. None of the comparisons are significant.

	Emphysema	Heart Problem	Cancer	Total
Smoker	145	140	300	585
Non-smoker	60	100	230	390
Total	205	240	530	975

Solution

a. Ho: p1 = p2 = p3                              Ha: Not all population proportions are equal

b)

240*390 / 975 = 96

b. 96

c)

The expected frequency of smokers with cancer is

530 *585 / 975 = 318

The expected frequency of non-smokers with emphysema is

390*205 / 975 = 82

The expected frequency of smokers with emphysema is

585*205 / 975 = 123