Chapter 9: Q.103 (page 554)

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.

Expert verified

(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

$H_{0} : μ = 4; H_{a} : μ < 4$

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

Test Statistic: $t = - 44.7$

$p - v a l u e = 0.0000$

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.

alpha	decision	reason for decision
0.01	Reject the null hypothesis.	$p - v a l u e < 0.01$

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

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

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