Question

A random sample of 60 life insurance policy holders showed that the average premiums paid on their life insurance policies was $340 per year with a standard deviation of $72. Construct a 80% confidence interval for he population mean. Round to the nearest tenths.​

Answer 1

To construct an 80% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (critical value) x (standard deviation / square root of sample size). Given the sample mean of $340, standard deviation of $72, and a sample size of 60, the 80% confidence interval for the population mean is approximately $329.4 to $350.6.

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the formula:

Confidence interval = sample mean ± (critical value) x (standard deviation / square root of sample size)

Given that the sample mean is $340, the standard deviation is $72, and the sample size is 60, we need to determine the critical value for an 80% confidence interval.

The critical value can be found using a t-distribution table or a calculator. For an 80% confidence level and a sample size of 60, the critical value is approximately 1.29.

Substituting the values into the formula, we have:

Confidence interval = $340 ± (1.29) x ($72 / √60)

Simplifying the calculation, we get:

Confidence interval = $340 ± $10.59

Rounding to the nearest tenths, the 80% confidence interval for the population mean is approximately $329.4 to $350.6.