Families in Poverty. In 2000, 8.6% of all U.S. families had incomes below the po

Question

Families in Poverty. In 2000, 8.6% of all U.S. families had incomes below the poverty level, as reported by the Census Bureau in Current Population Reports. During that same year, of 400 randomly selected families whose householder had at least a Bachelor's degree, 9 had incomes below the poverty level. At the 1% significance level, do the data provide sufficient evidence to conclude that, in 2000, the percentage of families that earned incomes below the poverty level was lower among those whose householders had at least a Bachelor's degree than among all U.S. families?

Explanation / Answer

Solution:

Here, we have to use the z test for population proportion. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: p = 0.086

Alternative hypothesis: Ha: p < 0.086

We are given a level of significance or alpha value = 1% or 0.01

The test statistic formula is given as below:

Z = (P – p) / sqrt(pq/n)

Where, P is sample proportion and p is population proportion.

Sample size = n and q = 1 – p = 1 – 0.086 =

We are given x = 9, n = 400

So, sample proportion = P = 9/400 = 0.0225

Z = (0.0225 – 0.086) / sqrt(0.086*0.914/400)

Z = -4.52982

P-value = 0.0000

Alpha value = 0.01

P-value < Alpha value

So, we reject the null hypothesis at 1% level of significance

So, we conclude that there is sufficient evidence that the percentage of families that earned incomes below the poverty level was lower among those whose householders had at least a Bachelor’s degree than among all U.S. families.

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