Question

In 2014, 15% of women 40-44 years of age have never given birth. A women’s health magazine conducts a more recent survey with a sample of 250 adult women 40-44 years of age. They found that 17.2% of the respondents have never given birth. An editor sees this result and believes that the proportion of women 40-44 years of age who have not given birth has increased since 2014. (Note: A labelled diagram and proper notation are required for part a).)
a) What is the probability that in a random sample of 250 adult women 40-44 years of age, more than 17.2% indicate they have never given birth? Interpret this probability.
b) Do you believe the editor is correct in claiming that the proportion of women 40-44 years of age who have not given birth has increased since 2014? Explain your answer using the result from part a)

Answer 1

Solution:

a) What is the probability that in a random sample of 250 adult women 40-44 years of age, more than 17.2% indicate they have never given birth? Interpret this probability.

Answer: We have to find:

Using the z-score formula, we have:

  

Now using the z-score formula, we have:

Therefore, the probability that more than 17.2% indicate they have never given birth is 0.1650

b) Do you believe the editor is correct in claiming that the proportion of women 40-44 years of age who have not given birth has increased since 2014? Explain your answer using the result from part a)

Answer: The editor is not correct in claiming that the proportion of women 40-44 years of age who have not given birth has increased since 2014 because the probability of seeing such a result is greater than 0.05