Question

A leading consumer magazine, The False Traders, claims that the small coffee sold at PHILZ coffee shop does not contain 12 ounces of coffee. A sample of 25 customers who purchased a small coffee yielded the following information:

- a sample mean of 12.10 ounces and a sample standard deviation of 0.25 ounces.

a. Set up a 95% confidence interval for the true population mean.

b. At the 10% level, test the alternate hypothesis that the true mean is not equal to 12 ounces.

Answer 1

(a) The 95% confidence interval for population mean is

where

degrees of freedom = 25-1=24

For 95% confidence with df = 24

critical value of t is , tc = 2.06 (from t table, critical value at 0.05 and df = 24)

Thus , 95% confidene interval for population mean is

= ( 11.897 , 12.203)

b)

The null and alternative hypothesis

12

12

Test statistic

12.10

S=0.25

  

= 2

df = n-1= 25-1=24

The two tailed critical value of t at 0.10 , with df =24 is tc = 1.71 (from t table)

Since calculated t > 1.71.

Reject H0

At 10% level of significance, there is sufficient evidence to conclude that mean is not equal to 12.