Question

In a sample of 80 Americans, 55% wished that they were rich. In a sample of 90

Europeans, 45% wished that they were rich.
a) At a = 0.01, is there difference in the proportions?
b) Find the 99% confidence interval for the differences of the two proportions

Answer 1

To determine if there is a difference in the proportions, we can conduct a hypothesis test. At a significance level of α = 0.01, we compare the test statistic to the critical value.

Step-by-step explanation:

To determine if there is a difference in the proportions, we can conduct a hypothesis test. Let's define the following:

• p1 = proportion of Americans wishing to be rich
• p2 = proportion of Europeans wishing to be rich

Our null hypothesis (H0) states that there is no difference between the proportions, so p1 = p2. The alternative hypothesis (Ha) states that there is a difference, so p1 ≠ p2. We can calculate the test statistic using this formula: Z = (p1 - p2) / √((p1(1-p1)/n1) + (p2(1-p2)/n2)), where n1 and n2 are the sample sizes.

At a significance level of α = 0.01, the critical value for a two-tailed test is ±2.576. If the test statistic falls within this range, we fail to reject the null hypothesis. Otherwise, we reject the null hypothesis.