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We have been given two ratios and we are supposed to compare our ratios whether they are proportional or not.
1. We will reduce our fractions to compare our ratios. Let us simplify each of our given fractions.
Let us divide numerator and denominator with greatest common factor. We can see that 21 is GCF of our ratio.
Now we will simplify our second ratio.
GCF of our fraction is 32. Upon dividing our fraction by 32 we will get,
We can see that our both ratios are similar.
2. Now we will find decimal values of our fractions.
We can see that .
Therefore, we can say that our ratios are proportional.
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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