In: Statistics and Probability
Popular belief states that individuals around the world are moving to the suburbs to live. According to the United Nations, the number of people living in urban areas is shown below.
Number of People |
Sample Size |
|
1950s |
30 |
100 |
2020s |
50 |
100 |
Source – Fortune, “Plotting the Rise of the Megacity”, March 2020, p. 82.
Data |
|
Hypothesized Difference |
0 |
Level of Significance |
0.05 |
Group 1 |
|
Number of Items of Interest |
30 |
Sample Size |
100 |
Group 2 |
|
Number of Items of Interest |
50 |
Sample Size |
100 |
Intermediate Calculations |
|
Group 1 Proportion |
0.30 |
Group 2 Proportion |
0.50 |
Difference in Two Proportions |
-0.20 |
Average Proportion |
0.4000 |
Z Test Statistic |
-2.8868 |
p-Value |
0.0039 |
Assuming that the population variances are equal, is there evidence of a difference in in the proportion of people living in urban areas in the 1950s and 2020s (a = .05)?
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As null hypothesis is rejected we conclude that the the proportion is significantly different of people living in are people living in urban areas in the 1950s and 2020s.
The conditions we need for inference on one proportion are:
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