Answer:
(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 - <em>α</em>)% confidence interval for population mean is:
Given:
Compute the critical value of <em>t</em> for 90% confidence level as follows:
*Use a <em>t-</em>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 <em>z</em> for 99% confidence level is:
Compute the sample size as follows:
Thus, the sample size required is 107.