Question

Milk has a pH of 6.7, which is slightly acidic. Cheesemakers add culture to milk to lower the pH, making it more acidic and turning it into cheese. A manufacturer is experimenting with a new culture that claims to produce a pH of 5.2, which is perfect for cheddar cheese. A set of 50 test batches resulted in an average pH of 5.11. A one-sample t-test was conducted to investigate whether there is evidence that the mean pH is different from 5.2. The test resulted in a p-value of 0.018. Which of the following is a correct interpretation of the p-value?

a. The probability that the true pH is equal to 5.2 is 0.018.
b. The probability that the true pH is different from 5.2 is 0.018.
c. The probability of observing a sample mean of 5.11 or less is 0.018 if the true mean is 5.2.
d. The probability of observing a sample mean of 5.11 or more is 0.018 if the true mean is 5.2.
e. The probability of observing a sample mean of 5.11 or less, or of 5.29 or more, is 0.018 if the true mean is 5.2.

Answer 1

e. The probability of observing a sample mean of 5.11 or less, or of 5.29 or more, is 0.018 if the true mean is 5.2.

Explanation:

We have a two-tailed one sample t-test.

The null hypothesis claims that the pH is not significantly different from 5.2.

The alternative hypothesis is that the mean pH is significantly different from 5.2.

The sample mean pH is 5.11, with a sample size of n=50.

The P-value of the test is 0.018.

This P-value corresponds to the probability of observing a sample mean of 5.11 or less, given that the population is defined by the null hypothesis (mean=5.2).

As this test is two-tailed, it also includes the probability of the other tail. That is the probability of observing a sample with mean 5.29 or more (0.09 or more from the population mean).

Then, we can say that, if the true mean is 5.2, there is a probability P=0.018 of observing a sample of size n=50 with a sample mean with a difference bigger than 0.09 from the population mean of the null hypothesis (5.11 or less or 5.29 or more).

The right answer is e.