Question

A barista at the Starbucks on Baltimore Avenue suspects the espresso machine is malfunctioning. Specifically, the barista believes the average temperature of cups of espresso is less than the company standard of 175 degrees F. To test their belief, the barista measures the temperatures for a random sample of cups of espresso. For the cups of espresso in the sample, the mean temperature equals 171.25 degrees F and the standard deviation equals 22.5 degrees F.

a. If the calculated value for the associated test statistic equaled −1.50, how many cups of espresso were in the sample the barista selected?

b. If the level of significance equals 0.10, what is the critical value of the associated test statistic?

c. Based on the test, should the barista call a repair person to fix the espresso machine?

Answer 1

a)
Let the mean temperature of the cups of espresso be
The company specified mean temperature is
We are to test:

We use the test statistic:

where,
s = sample standard deviation, given by:


Data given:
s = 22.5

T=-1.50







Hence, barista selected 81 samples.





b)
Here, since, population Standard Deviation is not available, we are to use t - distribution.

We reject H0 at level iff

where,
is the upper 100(1-)th percentile of the t - statistic with n-1 degrees of freedom.

Here, the critical value is:





c)
It is observed that,

Hence, H0 is rejected at 10% level of significance. That is, the barista is actually serving coffee at a temperature lower than . Hence, the barista should call in a repair person to fix the espresso machine.

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