Question

A quality control specialist for a restaurant chain takes a random sample of size 13 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.70 with a sample standard deviation of 1.58. Assume the underlying population is normally distributed. We wish to construct a 95% confidence interval for the true population mean for the amount of soda served.

What is the error bound? (Round your answer to two decimal places.)

Answer 1

Solution :

degrees of freedom = n - 1 = 13 - 1 = 12

t/2,df = t_0.025,12 = 2.179

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

= 2.179 * (1.58 / 13)

Margin of error = E = 0.95

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

  ± E  

= 13.70  ± 0.95

= ( 12.75, 14.65 )

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

= 2.179 * (1.58 / 13)

Margin of error = E = 0.95