Question

Molly works for a meat producer, and she needs to determine whether containers of ground beef have the correct fat content. She obtains a random sample of 120 containers of ground beef and finds that 84 percent have the correct fat content. Molly then conducts a hypothesis test of H0:p=0.80 versus Ha:p≠0.80 and calculates a test statistic of 1.10 with a p-value of 0.273. Which of the following best represents the meaning of the p-value?

A: If the population proportion is 0.84, the probability of observing a sample proportion of 0.80 is 0.273.
B: If the population proportion is 0.84, the probability of observing a sample proportion of at least 0.04 less than 0.84 is 0.273.
C: If the population proportion is 0.80, the probability of observing a sample proportion within 0.04 of 0.80 is 0.273.
D: If the population proportion is 0.80, the probability of observing a sample proportion at least 0.04 greater than 0.80 is 0.273.
E: If the population proportion is 0.80, the probability of observing a sample proportion of at least 0.84 or at most 0.76 is 0.273.

Answer 1

The correct answer is option (E)

Explanation:

Solution to the question

Let us recall from given question that,

H0:p=0.80

Ha:p≠0.80 (which is the two tailed test)

For the p-value we have,

P-value: Let us assume that the null hypothesis is true, then the probability of observing the sample statistics or the more extreme,

Therefore if p= 0.80, the probability of observing or detecting proportion of samples is of at least 0.84 or at most 0.76 is 0.273.