Respuesta :
Answer:
Test statistic
|Z| = 2.105632 > 1.96 at 0.05 level of significance
Null hypothesis is rejected at 0.05 level of significance
There is difference exist between the drug group and placebo group
Step-by-step explanation:
Step(i):-
Given each group was made up of 150 Hulks. 78 of them reported an improvement from the placebo group.
first sample proportion
[tex]p^{-} _{1} = \frac{78}{150} = 0.52[/tex]
Second sample proportion
[tex]p^{-} _{2} = \frac{96}{150} = 0.64[/tex]
a) Null Hypothesis : H₀ : There is no difference exist between the drug group and placebo group
H₀ : p₁ = p₂
Alternative Hypothesis : H₁ : There is difference exist between the drug group and placebo group
H₀ : p₁ ≠ p₂
b)
Step(ii):-
[tex]Z = \frac{p_{1} -p_{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } }) }[/tex]
where
[tex]P = \frac{n_{1} p^{-} _{1} + n_{2} p^{-} _{2} }{n_{1}+n_{2} }[/tex]
[tex]P = \frac{150 X 0.52+ 150 X 0.64}{150+150 }[/tex]
P = 0.58
Q = 1- P = 1- 0.58 = 0.42
[tex]Z = \frac{p_{1} -p_{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } }) }[/tex]
[tex]Z = \frac{0.52 -0.64}{\sqrt{0.58 X 0.42(\frac{1}{150 } +\frac{1}{150 } }) }[/tex]
Z = -2.105632
|Z| = |-2.105632| = 2.105632
Level of significance = 0.05
Z₀.₀₅ = 1.96
Final answer:-
|Z| = 2.105632 > 1.96 at 0.05 level of significance
Null hypothesis is rejected at 0.05 level of significance
There is difference exist between the drug group and placebo group
