Question

There was a lawsuit against Starbucks claiming that their lattes are being under filled. We know that a grande size cup should be 16 oz. The Today Show decided to do a test to see if they actually are being under filled. They went out and got 6 lattes and found that the average amount of liquid in each was 13.22 oz, with a sample standard deviation of 2.05. We are interested in determining if there is evidence that the lattes are being under filled. Use alpha= 0.01. The p-value is:

	a.	0.01 < p-value < 0.025
	b.	0.02 < p-value < 0.05
	c.	0.006
	d.	0.005< p-value < 0.01

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 16
Alternative Hypothesis, Ha: μ < 16

Rejection Region
This is left tailed test, for α = 0.01 and df = 5
Critical value of t is -3.365.
Hence reject H0 if t < -3.365

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (13.22 - 16)/(2.05/sqrt(6))
t = -3.322

P-value Approach
P-value = 0.0105

a.

0.01 < p-value < 0.025