Question

#17

There was a lawsuit against Starbucks claiming that their lattes are being underfilled. We know that a grande sized cup should be 16oz. The Today show decided to do a test to see if they are actually being underfilled, They went out and got 6 lattes and found of the average amount of liquid in each was 13.22oz, with a sample standard deviation of 2.05. We are interested in determining if there is evidence that the lattes are being underfilled. Use alpha = 0.01 what conclusion would be made here? Reject the null or don't reject the null?

Answer 1

Solution:

Claim: Starbucks lattes are being underfilled.

A grande sized cup should be 16oz.

That is: population mean =

Sample size = n   = 6

Sample mean =

Sample standard deviation = s = 2.05

Level of significance =

We have to test if there is evidence that the lattes are being underfilled.

Step 1) State H0 and H1:

Vs

( H1 is < type , since we have to test the lattes are being underfilled, thus this is left tailed test)

Step 2) Find t test statistic value:

Since sample size n = 6 is small and population standard deviation is unknown, we use t test statistic.

Step 3) Find t critical value:

df = n - 1 = 6 - 1 = 5

Left tail area =

Look in t table for df = 5 and one tail area = 0.01 and find t critical value.

From above t table, we can see t critical value = 3.365

Since this is left tailed test, t critical value = -3.365

Step 4) Decision rule:
Reject null hypothesis H0, if t test statistic value < t critical value = -3.365 , otherwise we fail to reject H0.

Since t test statistic value = -3.32 is not less than t critical value = -3.365 , we failed to reject H0,

That is: We do not reject the null hypothesis H0.

Step 5) Conclusion:

Since we failed to reject null hypothesis H0, at 0.01 level of significance, there is not enough evidence to conclude that the lattes are being underfilled.