The observed value of z (test statistic) is greater than 1.96 (the test statistic does fall into the rejection region), so Reject H₀ .
p₁ = the proportion of the non-smoker population who reply "yes"
p₂ = the proportion of the smoker population who reply "yes," then we are interested in testing the null hypothesis
H₀: p₁ = p₂
Alternate hypothesis:
Hₐ: p₁≠p₂
That implies then that the test statistic for testing:
H₀ : p1 = p2
Hₐ : p1 ≠ p2. (Two – tailed)
n1 = 605, y1 = 351
p1 = y1 / n1
= 351/605
≈ 0.58
n2 = 195, y2 = 41.
p2 = y2/n2
= 41 / 195
≈0.21
p = y1 + y2 / n1 + n2
= 351 + 41 / 605 + 195
= 392 / 800
= 0.49
The test statistic is
z =
= 8.988
critical region for α = 0.01
z = 2.576
The observed value of z (test statistic) is greater than 1.96 (the test statistic does fall into the rejection region),
so Reject H₀ .
To learn more about hypothesis testing from the given link
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