A recent survey was conducted with a simple random sample of 35 shoppers at the food court in a local mall. The mall claims that the mean price for lunch is less than $4.65. The mean of the sample is $4.49, and the standard deviation of the population of lunch shoppers is $0.36. A P-value of 0.0043 is found using a 0.01 significance level to test the claim that the mean price for lunch is less than $4.65. State the conclusion about the null hypothesis.

Question

A) accept the null hypothesis
B) fail to accept the null hypothesis
C) reject the null hypothesis
D) fail to reject the null hypothesis

GPT-4o mini · Answer

To determine the conclusion about the null hypothesis, we need to consider the P-value in relation to the significance level.

The claim being tested is that the mean price for lunch is less than $4.65, which can be stated as:

Null Hypothesis ($H_0$): $\mu \geq 4.65$ (the mean price is greater than or equal to $4.65)
Alternative Hypothesis ($H_a$): $\mu < 4.65$ (the mean price is less than $4.65)

You have a P-value of 0.0043 and a significance level ($\alpha$) of 0.01.

Since the P-value (0.0043) is less than the significance level (0.01), we reject the null hypothesis.

Thus, the correct conclusion is:

C) reject the null hypothesis.