Answer:
The minimum sample size required is 4610.
Explanation:
The (1 - α)% confidence interval for population proportion p is:

The margin of error for this interval is:

It is provided that a 99% confidence interval is computed to estimate the percentage of homeowners who own at least two television sets.
Assume that 50% of the homeowners own at least two television sets.
So, the sample proportion is,
.
The critical value of z for 99% confidence interval is:

*Use a z-table for the critical value.
The margin of error is given as, MOE = 0.019.
Compute the value of n as follows:

![n=[(z_(\alpha/2)* √(\hat p(1-\hat p)) )/(MOE)]^(2)](https://img.qammunity.org/2021/formulas/mathematics/college/u8xrlsot42hymhv1r8tf3bn36vnxzmeeby.png)
![=[(2.58* √(0.50(1-0.50)))/(0.019)]^(2)](https://img.qammunity.org/2021/formulas/mathematics/college/xyilyvkxod5jgtxv6fcw7dutt16ui6ni27.png)

Thus, the minimum sample size required is 4610.