Question

A quality control specialist for a restaurant chain takes a random sample of size 10 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.20 with a sample standard deviation of 1.51. Assume the underlying population is normally distributed.
Find the 95% confidence interval for the true population mean for the amount of soda served.

Answer 1

Solution :

t_{$\alpha$ /2,df} = 2.262

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

= 2.262 * (1.51 / $\sqrt$ 10)

Margin of error = E = 1.08

The 95% confidence interval estimate of the population mean is,

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

13.20 - 1.08 < $\mu$ < 13.20 + 1.08

12.12 < $\mu$ < 14.28

(12.12 , 14.28)