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.

Short answer

(0.60 years, 0.90 years) or approximately (7.2 months, 10.8 months), when the sample standard deviation is rounded to 0.33.

Step-by-step solution

Find H0 and Ha: We want to test if if the mean weaning age in the U.S. is less than four years old. 

$H_0:\mu =4;H_a:\mu <4$

Determine the distribution needed: In words, CLEARLY state what your random variable represents.  Let μ represent the mean age at which American mothers wean their children

Normal:$N\left(4,\frac{0.333}{\sqrt{21}}\right)$

Test Statistic:$t=–44.7$

Calculate the p-value using the normal distribution for mean RV

$p-value=0.0000$

In one to two complete sentences, explain what the p-value means for this problem.

If the null hypothesis is true (the mean age is 4), then there is a 0.0000 probability that the sample (estimated) mean age is 3 or more.

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alpha	decision	reason for decision
0.01	Reject the null hypothesis.	$p-value<0.01$

Conclusion: There is sufficient evidence to conclude that the mean age at which American mothers wean their children is less than four years old.

Confidence Interval

(0.60 years, 0.90 years) or approximately (7.2 months, 10.8 months), when the sample standard deviation is rounded to 0.33.