Question

A leading consumer magazine, The False Traders, claims that the small coffee sold at Beanz 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

x̅ = 12.1, s = 0.25, n = 25  

a)

95% Confidence interval :  

At α = 0.05 and df = n-1 = 24, two tailed critical value, t-crit = T.INV.2T(0.05, 24) = 2.064

Lower Bound = x̅ - t-crit*s/√n = 12.1 - 2.064 * 0.25/√25 = 11.997

Upper Bound = x̅ + t-crit*s/√n = 12.1 + 2.064 * 0.25/√25 = 12.203

b)

Null and Alternative hypothesis:

Ho : µ = 12 ; H1 : µ ≠ 12

Test statistic:

t = (x̅ - µ)/(s/√n) = (12.1 - 12)/(0.25/√25) = 2.0

df = n-1 = 24

p-value = T.DIST.2T(ABS(2), 24) = 0.0569

Decision:

p-value < α, Reject the null hypothesis.

Conclusion:

There is enough evidence to conclude that the true mean is not equal to 12 ounces at 0.10 significance level.