Question

Thirty-seven items are randomly selected from a population of 390 items. The sample mean is 36, and the sample standard deviation 10. Develop a 90% confidence interval for the population mean. (Round the t-value to 3 decimal places. Round the final answers to 2 decimal places.)  

The confidence interval is between  and  .

Answer 1

Solution :

Given that,

t /2,df = 1.688

Margin of error = E = t/2,df * (s /n)

= 1.688 * (10 / 37)

Margin of error = E = 2.78

The 90% confidence interval estimate of the population mean is,

- E < < + E

36 - 2.78 < < 36 + 2.78

33.22 < < 38.78

The confidence interval is between 33.22 and 38.78