It is not possible to construct a confidence interval estimate of the population mean if the population variance is unknown.Group of answer choicesTrueFalse

False.

Here's a step-by-step explanation:

1. Even if the population variance is unknown, it is still possible to construct a confidence interval estimate of the population mean.

2. When the population variance is unknown, a common approach is to use the sample variance instead as an estimate of the population variance.

3. In such cases, instead of using a Z-distribution which assumes known population variance, a t-distribution is used. The t-distribution is a type of probability distribution that is symmetric and bell-shaped, like the standard normal distribution, but has heavier tails, which makes it more suitable for small sample sizes and when the population variance is unknown.

4. The formula for the confidence interval in this case becomes: sample mean ± (t-value * standard error), where the standard error is calculated using the sample standard deviation (square root of the sample variance) and the sample size.

5. Therefore, it is not true that it is impossible to construct a confidence interval estimate of the population mean if the population variance is unknown.