In 2000, the United Nations Claimed That There Was a Higher

Question

Examlex · Accepted Answer

The Answer is With the conditions satisfied (from Problem 1), the sampling distribution of the difference in proportions is approximately Normal with a mean of pm - pw, the true difference between the population proportions.
We can find a two-proportion z-interval.
We know:

n_{m}=234, \hat{p}_{m}=0.192, n_{w}=251, \hat{p}_{w}=0.167

We estimate

S D\left(\hat{p_{m}}-\hat{p_{w}} ight)

as

S E\left(\hat{p}_{m}-\hat{p}_{w} ight)=\sqrt{\frac{\hat{p}_{m} \hat{q}_{m}}{n_{m}}+\frac{\hat{p}_{w} \hat{q}_{w}}{n_{w}}}=\sqrt{\frac{(0.192)(0.808)}{234}+\frac{(0.167)(0.833)}{201}}=0.0349

\begin{array}{l}M E=z^{*} imes S E\left(\hat{p_{m}}-\hat{p}_{w} ight)=1.96(U .0349)=0.0684 \\end{array}

The observed difference in sample proportions = pm - pw = 0.192 - 0.167 = 0.025, so the 95% confidence interval is 0.025 ± 0.0684, or -4% to 9%. We 95% confident that the proportion of illiterate men in Qatar is between
4-percentage points
lower and 9-percentage points higher than the proportion of illiterate women.
According to the 2010 census, 20.3% of the population of the United States (ages 5 and up) live in a home in which a language other than English is spoken. Advocates for providing government programs to assist non-English speakers are convinced that, with the increasing non-white population in the United States, this proportion has probably increased. They plan to conduct a survey, and if they find the proportion of people who live in such homes has increased, they will organize a campaign to increase government investment in these assistance programs.

In 2000, the United Nations Claimed That There Was a Higher

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