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:
<em>H₀</em>: There is no difference between the two proportions, i.e. <em>p</em>₁ - <em>p</em>₂ = 0.
<em>Hₐ</em>: There is a significant difference between the two proportions, i.e. <em>p</em>₁ - <em>p</em>₂ ≠ 0.
The information provided is:
n₁ = 40
n₂ = 40
X₁ = 36
X₂ = 16
Compute the sample proportions and total proportions as follows:
Compute the test statistic value as follows:
![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](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B%5Chat%20p_%7B1%7D-%5Chat%20p_%7B2%7D%7D%7B%5Csqrt%7B%5Chat%20P%281-%5Chat%20P%29%5B%5Cfrac%7B1%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7B1%7D%7Bn_%7B2%7D%7D%5D%7D%7D%3D%5Cfrac%7B0.90-0.40%7D%7B%5Csqrt%7B0.65%281-0.65%29%5B%5Cfrac%7B1%7D%7B40%7D%2B%5Cfrac%7B1%7D%7B40%7D%5D%7D%7D%3D4.69)
The test statistic value is 4.69.
The decision rule is:
The null hypothesis will be rejected if the <em>p</em>-value of the test is less than the significance level.
Compute the <em>p</em>-value as follows:
The <em>p</em>-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.
