Question

According to a Gallup poll in October 2015, having young children at home greatly influences whether women in the U.S. prefer to stay at home or work outside of it. More than half of women, 55%, who have a child younger than 18 would ideally like to stay home and care for their house and family, while 58% of those without young children would rather work outside the home. Having young children makes little difference in men's preferences, with close to three-quarters preferring to work regardless of their parenting status. Gallup states that their method has a margin of error of 0.031.

(a) Give a point estimate for the proportion of all US women with a child under 18 that would like to stay at home.



(b) Give an interval estimate for the proportion of all US women with a child under 18 that would like to stay at home. Use three decimal places in your answer.

Answer 1

a) 0.55

b) (0.519, 0.581)

Explanation:

a) The point estimate is a single value used to approximate a population parameter. The best point estimate for a population proportion is the sample proportion which in this case is 55%.

b) The interval estimate for the population proportion is going to be:

(Ps - E, Ps + E)

Where Ps is the sample proportion and E is the margin of error. In this case the interval estimate is going to be:

(0.55 - 0.031, 0.55 + 0.031)

= (0.519, 0.581)