Question

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)?

State the null hypothesis
State the alternative hypothesis
What critical values should be used?
What is the test statistic?
What is the p-value?
Interpret the meaning of the p-value
Should the null hypothesis be rejected
What is the conclusion?
State one of the assumptions needed

Answer 1

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:

• Random: The data needs to come from a random sample or randomized experiment.
• Normal: The sampling distribution of population proportion p^​ needs to be approximately normal — needs at least 10 expected successes and 10 expected failures.
• Independent: Individual observations need to be independent. If sampling without replacement, our sample size shouldn't be more than 10% percent of the population.

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