Question

In a survey, 1,000 mothers and fathers are asked about the importance of sports for boys and girls. Of the parents interviewed, 75% said genders are equal and should have equal opportunities to participate in sports. Assuming that .75 is correct for the population, what are the mean, standard deviation, and shape of the distribution of the sample proportion p with hat on top for n = 100? .75, .0433, approximately normal .75, .00433, approximately normal .75, .25, symmetric but not normal .75, .0137, approximately normal .75, .0433, symmetric but not normal

Answer 1

This distribution has mean=0.75, standard deviation=0.0433 and approximately normal.

Explanation:

We need to estimate the mean, standard deviation and shape of the distribution of the values of the sample proportions (p-hat) in repeated samples of size n=100.

The sample mean is expected to be the same as the population mean

`\bar{p}=0.75`

The standard deviation can be calculated as:

`\sigma=\sqrt{(p*(1-p))/(n) } =\sqrt{(0.75*(1-0.75))/(100) }= 0.0433`

The distribution is symmetrical, and it looks like approximately normal for this sample size.

So we can conclude this distribution has mean=0.75, standard deviation=0.0433 and approximately normal.