Question

Suppose Jamal is studying poverty in his economics class, and he wants to compare the proportion of individuals living below the poverty line in the western United States in different years. He collects data on a simple random sample of people from 2013 and a simple random sample of people from 2014. His data are summarized in the table.

Population	Population description	Sample size	Number of successes	Proportion of sucesses
1	population in 2013	n1=486	X1=74	^p1=0.15226
2	population in 2014	n2=490	X2=69	^p2=0.14082

Jamal wants to run a two-sample z‑test for the difference of two proportions to test the alternative hypothesis, H1:p1>p2, against the null hypothesis, H0:p1=p2, where p1 is the proportion of population in 2013 that are living below the poverty line, and p2 is the proportion of population in 2014 that are living below the poverty line. Jamal selects a significance level of α=0.10.

Compute the z‑statistic and P-value for Jamal’s z‑test for the difference of two proportions, p1−p2. Give your answers precise to three decimal places.

Based on your answers and a significance level of α=0.10, complete the following sentences to state the decision and conclusion of Jamal’s test.

Source: adapted from DeNavas-Walt, Carmen and Bernadette D. Proctor. Income and Poverty in the United States: 2014. Table 3. People in Poverty by Selected Characteristics: 2013 and 2014 [Online]; U.S. Census Bureau, Current Population Reports: U.S. Government Printing Office, Washington, DC, 2015; P60-252. https://www.census.gov/content/dam/Census/library/publications/2015/demo/p60-252.pdf (accessed September 11, 2016).

Jamal decides                                                                           the                                                                          

hypothesis. The conclusion is that                                                                            the proportion of the 2013 population

living in poverty                                                                           the proportion of the 2014 population living in

poverty, because                                                                             .

Answer Bank

compared to

is the same as

that no decision can be made about

no conclusion can be drawn about

alternative

null

the test requirements have not been met

there is sufficient evidence that

to reject

to fail to reject

there is insufficient evidence that

is higher than

the difference is statistically significant (P<0.10)

is different than

the difference is not statistically significant (P>0.10)

is less than

accept

Answer 1