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. Also conduct a hypothesis test summary.

Answer 1

Answer :

we have given :

n  = sample size  = 21

x̄ = sample mean  = 9 month

s = sample  standard deviation  = 4 month  

μ = population mean = 4 year = 48 month

α = 5 % = 0.05

Claim  : Conduct a hypothesis test to determine if the mean weaning age in the U.S.

is less than four years old.

## step1 : null and alternative Hypothesis :

Ho : μ  ≥   4 year vs H1: μ   < 4 year

( it is left  tailed  , one tailed test )

## step 2 : Test statistics :

t = (x̄ - μ) *√ n / s

t   = ( 9  - 48  ) * √ 21  / 4

= - 178.7204   / 4

= - 44 .6801

## step 3 :  level of significance  = 0.05

## step 4 : critical value

df = degree of freedom = n - 1 = 20

critical value = t ( α , df )

=   - 1.7247 from table , ( it is left tailed test )  

step 5 : Decision  :

We reject Ho if - t statistics <  - t critical value here - t statistics   <   - t critical value  

we reject Ho at given level of significance .

Step 6 : Conclusion :

There is Sufficient evidence to conclude that   the mean weaning age in the U.S. is less than four years old.