Question

La Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five worldwide. In America, most nursing mothers wean their children much earlier. Suppose a random survey is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was nine months (3/4 year) with a standard deviation of 4 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old.

a. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is equal to four years.

b. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is not equal to four years.

c. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years.

d. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is greater than four years.

Answer 1

The hypothesis test aims to compare the sample mean weaning age of U.S. children to the worldwide average reported by La Leche League International. Given the sample mean of nine months, the null hypothesis (equal to four years) would likely be rejected in favor of the alternative hypothesis that the mean age is less than four years.

Step-by-step explanation:

To conduct a hypothesis test regarding the mean weaning age of U.S. children, we must follow certain steps. We will be testing the null hypothesis, which states that the mean age is equal to four years (the hypothesized worldwide average), against alternative hypotheses that it is not equal to, less than, or greater than four years.

Steps for Hypothesis Testing-

1. State the null hypothesis (H0) and the alternative hypothesis (H1).
   
2. Determine the test statistic using the sample mean, standard deviation, and sample size. Since we have a small sample size (n = 21), we should use the t-test:
3. Calculate the p-value associated with the test statistic, which indicates the probability of observing the data if the null hypothesis is true.
4. Compare the p-value to the chosen level of significance (α), and reject the null hypothesis if the p-value is less than α. A common significance level is 0.05.

Given that the sample mean reported is nine months, which is significantly less than four years, it is very likely the tests will result in rejecting the null hypothesis in parts a, b, and c, confirming that the mean weaning age in the U.S. is indeed less than four years.

As for part d, since the sample mean is already lower than four years, there is no need to prove that it is greater; thus, the H1 for part d would not be supported.