Question

In clinical trials of a newly developed cold medicine, it was found that 45 out of 200 individuals that took the new medicine (Group 1) experienced an upset stomach as a side effect and 33 out of 150 individuals that took a placebo (Group 2) experienced an upset stomach. Test to see if the new drug produced a significantly higher proportion of individuals experiencing upset stomach. Use a 0.01 level of significance. Select the correct alternative hypothesis and decision.

a. H: Pi≠P2; Do not reject the null hypothesis.
b. H1: p1>P2; Do not reject the null hypothesis.
c. H: Pi > p2; Reject the null hypothesis.
d. H1: p. e.) Hi: p1≠P2; Reject the null hypothesis.
f. H: P1

Answer 1

Explanation:

Group 1 Information:

sample size : n₁ = 200

individuals with stomach as a side effect x₁ = 45

p₁ = 45 / 200 p₁ = 0,225 then q₁ = 1 - p₁ q₁ = 0,775

Group 2 Information:

sample size : n₂ = 150

individuals with stomach as a side effect x₂ = 33

p₂ = 33/150 p₂ = 0,22 q₂ = 0,78

Hypothesis Test:

Null Hypothesis: H₀ p₁ = p₂

Alternative Hypothesis Hₐ p₁ > p₂

The alternative hypothesis indicates that the test is a one-tail test to the right

Significance level is α = 0,01 ( confidence interval 99%)

From z-table we get z(c) for that α z(c) = 2,32

To calculate z(s)

z(s) = ( p₁ - p₂ ) / EED

EED = √ ( p₁*q₁)/n₁ + ( p₂*q₂)/n₂

EED = √ ( 0,225*0,775)/200 + (0,22*0,78)/150

EED = √ 0,0008718 + 0,001144

EED = 0,045

z(s) = ( 0,225 - 0,22 ) / 0,045

z(s) = 0,005 / 0,045

z(s) = 0,11

Comparing z(s) and z(c)

z(s) < z(c) 0.11 < 2.32

Then z(s) is in the acceptance region. We accept H₀ . We don´t have evidence to support differences between the two groups.