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, 57%, 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.

1. Give a point estimate for the proportion of all US women with a child under 18 that would like to stay at home.
2. Give an interval estimate for the proportion of all US women with a child under 18 that would like to stay at home.
3. What is the difference between a point estimate and an interval estimate?
A. 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.
B. 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.
C. 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.
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 parameter​ value; an interval estimate also gives us a plausible range of values for the parameter.

Answer 1

a

`\^p = 0.57`

b

`0.539 <p< 0.601`

c

The correct option is C

Explanation:

The percentage of women who would like to stay at home and take care of their family due to the fact that they have a child younger than 18 is
`p_1  =  57\%`

The percentage of women who would rather work outside their home due to the fact that they don't have children is
`p_2 =   58\%`

The margin of error is
`E = 0.031`

Gnerally the point estimate of all US women with a child under 18 that would like to stay at home is mathematically represented as

`\^ p =  (57)/(100)`

`\^ p = 0.57`

Gnerally the interval estimate for the proportion of all US women with a child under 18 that would like to stay at home is mathematically as

`\^ p -E  < p <  \^ p +E`

=>
`0.57 -0.031 <p<  0.57 + 0.031`

=>
`0.539 <p< 0.601`