Respuesta :
Answer:
It can be concluded that the medicated lotion has an effect on treating skin irritations.
Step-by-step explanation:
In this case we need to determine whether the medicated lotion was effective in treating the skin irritation or not.
The hypothesis can be defined as follows:
H₀: There is no difference between the two proportions, i.e. p₁ - p₂ = 0.
Hₐ: There is a significant difference between the two proportions, i.e. p₁ - p₂ ≠ 0.
The information provided is:
n₁ = 40
n₂ = 40
X₁ = 36
X₂ = 16
Compute the sample proportions and total proportions as follows:
[tex]\hat p_{1}=\frac{36}{40}=0.90\\\\\hat p_{2}=\frac{16}{40}=0.40\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{36+16}{40+40}=0.65[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}=\frac{0.90-0.40}{\sqrt{0.65(1-0.65)[\frac{1}{40}+\frac{1}{40}]}}=4.69[/tex]
The test statistic value is 4.69.
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
Compute the p-value as follows:
[tex]p-value=2\times P(Z<4.69)<0.00001[/tex]
The p-value of the test is very small.
The null hypothesis will be rejected at any significance level.
Thus, there is a significant difference between the two proportions.
So, it can be concluded that the medicated lotion has an effect on treating skin irritations.
