A study reported that 53% of men age 62-64 were still working, 36% of women age 62 to 64 were still working, 31% men age 65 to 69 were still working, and 22% of women age 65 to 69 were still working. Suppose that the study was based on a sample size of 100 in each group. Complete parts a-c.

a. Is there evidence of a significant difference among the groups with respect to the proportion who are still working? Use

alpha equals 0.05

-xstat squared =

xstat alpha =

pvalue =

critical value =

conclusion =

state the null and alternative hypotheses.

a. H ₀ : π ₁ = π ₂ = π ₃ = π ₄

H ₁ : π _{1 ≠} π _{2 ≠} π _{3 ≠} π ₄

b. H ₀ : π ₁ = π ₂ = π ₃ = π ₄ = 0

H ₁ : π ₁ ≠ π ₂ ≠ π ₃ ≠ π ₄ ≠ 0

c. H ₀ : π ₁ = π ₂ = π ₃ = π ₄ = 0

H _1: At least one of the π _j is not equal to zero (where j = 1, 2 , 3, 4)

d. H ₀ : π ₁ = π ₂ = π ₃ = π ₄

H _1: Not all π _j are equal (where j = 1, 2 , 3, 4)

Test statistic is c ² _STAT = ____