Question

2. 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.

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

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

Answer 1

Solution :

Point estimate = sample mean = = 12.10

sample standard deviation = s = 0.25

sample size = n = 25

Degrees of freedom = df = n - 1 = 25-1 = 24

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

t/2,df = t0.025, 24 = 2.06

t /2,df = 2.06

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

= 2.06 * (0.25 / 25)

Margin of error = E = 0.103

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

- E < <  + E

12.10 -0.103 < < 12.10 +0.103

11.997 < < 12.203

(11.997 ,12.203)

= 12

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 12

Ha : 12

Test statistic = t

= ( - ) / s/ n

= (12.10-12) /0.25 / 25

= 2

p(Z >2 ) = 1-P (Z < 2) =0.0569

P-value = 0.0569

= 0.10

0.0569 < 0.10

Reject the null hypothesis .

There is sufficient evidence to suggest that the true mean is not equal to 12 ounces, at the 0.10 significance level.