Suppose Jamal is studying poverty in his economics class, and hewants to compare the proportion of individuals living below thepoverty line in the western United States in different years. Hecollects data on a simple random sample of people from 2013 and asimple random sample of people from 2014. His data are summarizedin 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 twoproportions to test the alternative hypothesis, H1:p1>p2,against the null hypothesis, H0:p1=p2, where p1 is the proportionof population in 2013 that are living below the poverty line, andp2 is the proportion of population in 2014 that are living belowthe poverty line. Jamal selects a significance level of α=0.10.
Compute the z‑statistic and P-value for Jamal’s z‑test for thedifference of two proportions, p1−p2. Give your answers precise tothree decimal places.
Based on your answers and a significance level of α=0.10,complete the following sentences to state the decision andconclusion 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                                                                        Â
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
