Question

15) 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 8 months (2/3 year) with a standard deviation of 2 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old. Conduct a hypothesis test at the 5% level.

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Enter your answers in years. Round your answers to four decimal places.)

Answer 1

Here we are assuming that the population is normally distributed.(this fact is also true since the population size is large as the population is the U.S. mithers who recently weaned their children. since also sample is random and population standard deviation is unknown, and sample size is not so large to apply z-test, therefore all conditions to apply t-test are meet. here we are testing that the mean weaning age in the U.S. is less than four years old mean less than 4*12=48 months.

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