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, 58%, 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.

(c) What is the difference between a point estimate and an interval estimate?

A)A point estimate only tells us the parameter​ value; an interval estimate also gives us a measure of how far away that guess is likely to be from the parameter.

B) A point estimate only tells us the parameter​ value; an interval estimate also gives us a plausible range of values for the parameter.   

C) A point estimate only tells us the best guess for the​ parameter; an interval estimate is more likely to be close to the parameter than a single point.

D) A point estimate only tells us the parameter​ value; an interval estimate also gives us a plausible range of values for the statistic.

E) A point estimate only tells us the best guess for the​ parameter; an interval estimate also gives us a measure of how far away that guess is likely to be from the parameter.

Answer 1

It is given that 58% of the women who have a child younger than 18 would ideally like to stay home and care for their house and family.Hence,

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

(b) The interval estimate for the proportion of all US women with a child under 18 that would like to stay at home can be obtained using the formula:

where, is the point estimate based on the sample and n is the sample size. Z is the Z score corresponding to alpha level of significance.

................................... (ME = Margin of Error)

(c) Both point and interval estimate provide a guess for the population parameter based on the sample. Hence Options B,D and E can be omitted as they claim that point estimate gives the parameter value itself, which is often not the case.

Although, the point estimate provides an exact value that is usually easy to interpret, the claim might not always be true.Hence, it would be a better option if, we have in hand, a range of probable values for the parameter i.e. an interval, which gives us more confidence on our precision of our estimate.  

The best suited option would be:

C) A point estimate only tells us the best guess for the​ parameter; an interval estimate is more likely to be close to the parameter than a single point.