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**

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