Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021

Which of the following is the most appropriate conclusion?

a. There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds.
b. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 14 pounds in 2015.
c. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 16 pounds in 2015.
d. There is 2.1% chance that the population of expectant mothers will have a mean weight increase of 16 pounds or greater in 2015 if the mean second trimester weight gain for all expectant mothers was 14 pounds in 1959.

Option A - There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds.

Answer Link

joaobezerra joaobezerra · Answer 2 · 2021-11-09T14:04:59+01:00

The correct interpretation of the p-value is of:

a. There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds.

At the null hypothesis, we test if the mean weight increase is of 14 pounds or less, that is:

[tex]H_0: \mu \leq 14[/tex]

At the alternative hypothesis, we test if the mean weight increase is of more than 14 pounds, that is:

[tex]H_1: \mu > 14[/tex].

The sample mean is of 16 pounds.
We are testing if the mean is greater than a value, which is a right-tailed test, thus the p-value is the probability of finding a sample mean abode the one found, that is, the probability of finding a sample mean above 16 pounds, considering that the mean weight gain is still of 14 pounds.

In this problem, p-value of 0.021, thus the correct interpretation is:

a. There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds.

A similar problem is given at https://brainly.com/question/13873630