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:
![\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](https://tex.z-dn.net/?f=%5Chat%20p_%7B1%7D%3D%5Cfrac%7B36%7D%7B40%7D%3D0.90%5C%5C%5C%5C%5Chat%20p_%7B2%7D%3D%5Cfrac%7B16%7D%7B40%7D%3D0.40%5C%5C%5C%5C%5Chat%20P%3D%5Cfrac%7BX_%7B1%7D%2BX_%7B2%7D%7D%7Bn_%7B1%7D%2Bn_%7B2%7D%7D%3D%5Cfrac%7B36%2B16%7D%7B40%2B40%7D%3D0.65)
Compute the test statistic value as follows:
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:
![p-value=2\times P(Z](https://tex.z-dn.net/?f=p-value%3D2%5Ctimes%20P%28Z%3C4.69%29%3C0.00001)
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.