Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1,000.a. Based on this sample information, develop a 90 percent confidence interval for thepopulation mean yearly premium. b. How large a sample is needed to find the population mean within $250 at 99 percentconfidence?

(a) The 90 percent confidence interval for the population mean yearly premium is ($10,974.53, $10983.47).

(b) The sample size required is 107.

Step-by-step explanation:

(a)

The (1 - α)% confidence interval for population mean is:

Given:

Compute the critical value of t for 90% confidence level as follows:

*Use a t-table.

Compute the 90% confidence interval for population mean as follows:

Thus, the 90 percent confidence interval for the population mean yearly premium is ($10,974.53, $10983.47).

(b)

The margin of error is provided as:

MOE = $250

The confidence level is, 99%.

The critical value of z for 99% confidence level is:

Compute the sample size as follows:

Thus, the sample size required is 107.

step-by-step explanation:

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step-by-step explanation: