Question

A simple random sample with n = 58 provided a sample mean of 26.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.) (a) Develop a 90% confidence interval for the population mean. 25.5 to 27.5 (b) Develop a 95% confidence interval for the population mean. to 27.7 25.3 (C) Develop a 99% confidence interval for the population mean. 24.9 x to 28.1 x

Answer 1

Solution :

Given that,

(c)

t$\alpha$ /2,df = 2.665

Margin of error = E = t$\alpha$/2,df * (s /$\sqrt$n)

= 2.665 * (4.4 / $\sqrt$ 58)

Margin of error = E = 1.5

The 99% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

26.5 - 1.5 < $\mu$ < 26.5 + 1.5

25 < $\mu$ < 28

A 99% confidence interval for the population mean 25 to 28