Answer:
The minimum sample size required is 49.
Explanation:
The (1 - α)% confidence interval for the difference between two proportions is:

*The sample size is considered equal in this case.
The width of the interval is at most 0.40.
Then the margin of error of the interval will be:
MOE = Width ÷ 2 = 0.20
The formula of the margin of error is:

Assume that the two sample proportion values are 0.50.
The critical value of z for 95% confidence level is:

Compute the sample size required as follows:

![n=[\frac{z_(\alpha/2)* \sqrt{\hat p_(1)(1-\hat p_(1))+\hat p_(2)(1-\hat p_(2))}}{MOE}]^(2)](https://img.qammunity.org/2021/formulas/mathematics/college/t1nzfwicx8uhamtafbwnwxknsateriqkfe.png)
![=[(1.96* √(0.50(1-0.50)+0.50(1-0.50)))/(0.20)]^(2)\\\\=48.02\\\\\approx 49](https://img.qammunity.org/2021/formulas/mathematics/college/464nlrzhae82s1b2jywyhls1a3xulokc3f.png)
Thus, the minimum sample size required is 49.