It is not possible to construct a confidence interval estimate of the population mean if the population variance is unknown.Group of answer choicesTrueFalse
Question
It is not possible to construct a confidence interval estimate of the population mean if the population variance is unknown.Group of answer choicesTrueFalse
Solution
False.
Here's a step-by-step explanation:
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Even if the population variance is unknown, it is still possible to construct a confidence interval estimate of the population mean.
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When the population variance is unknown, a common approach is to use the sample variance instead as an estimate of the population variance.
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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.
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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.
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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.
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