Question

A researcher wants to test the hypothesis that college students weigh less on average than the average American (160 lbs). The sample mean of the 80 students who were weighed was found to be 142 pounds and the p-value was 0.03. This means that if the mean of all students’ weight is 160 lbs, then there would be only a 3% chance that a randomly selected group of 80 students would have a mean weight of less than 142 lbs.True or False.

Answer 1

Answer: True.

Explanation:

Let
`\mu` be the population mean.

Given : Null hypothesis =
`H_0:\mu=160`

Alternative hypothesis =
`H_1:\mu<160`

Since , the alternative hypothesis is left-tailed, then the test is a left-tailed test.

The sample mean (
`\overlien{x}`) of the 80 students who were weighed was found to be 142 pounds and the p-value was 0.03.

We know that p-value gives that probability that if the null hypothesis is true, than the sample mean (
`\overlien{x}`) will be at least as small as the actual mean (
`\mu`).

It means that if the mean of all students’ weight is 160 lbs, then there would be only a 3% chance that a randomly selected group of 80 students would have a mean weight of less than 142 lbs.

Hence, the answer is "True".