Question

Please show all work

Suppose you randomly sample 49 cans and find the mean amount of Coke in this sample is 11.85 ounces and the standard deviation is 0.30 ounces.

Construct a 95% confidence interval estimate for the mean amount of Coke in the all such cans.

Answer 1

Solution :

Given that,

= 11.85 ounce

s = 0.30 ounces.

n = 49

Degrees of freedom = df = n - 1 = 49 - 1 = 48

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,48 = 2.011

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

= 2.011 * (0.30 / 49)

= 0.09

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

- E < < + E

11.85 - 0.09 < < 11.85 + 0.09

11.76 < < 11.94

(11.76, 11.94 )