Families USA, a monthly magazine that discusses issues related to health and hea
ID: 3261514 • Letter: F
Question
Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 19 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10, 350. The standard deviation of the sample was $955 (Use t Distribution Table.) a. Based on this sample information, develop a 95% confidence interval for the population mean yearly premium. (Round your answers to the nearest whole number.) Confidence interval for the population mean yearly premium is between $ ______ and $ ______ b. How large a sample is needed to find the population mean within $225 at 90% confidence? (Round up your answer to the next whole number.) Sample size _________
Explanation / Answer
a)
margin of error = z-sscore * std/sqrt(n)
= 1.96 * 955/sqrt(19)
= 429.42
=>
confidence interval is between 10350 - 429.42 and 10350 + 429.42 which is between
9921 and 10779
b)
margin of error = 225
=>
1.96 * 955/sqrt(n) = 225
size of sample n = 70
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