Question

According to the Census Bureau’s American Housing Survey, the primary reason people who move close their new neighborhood is because the location is convenient to work. Based on 1990 Census Bureau data, we know that 24% of the population of people who moved selected “location convenient to work” as the reason for selecting their new neighborhood. Assume a sample of 300 people who moved during 2003 found 93 did so to be closer to work.

1. Does the sample data support the research conclusion that in 2003 more people are choosing where to live based on how close they will be to their work?

2. Using α = 0.05 what is your research conclusion?

Answer 1

Let p denotes the true proportion of the population of people who moved selected “location convenient to work” as the reason for selecting their new neighborhood.

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

and P-value

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that sample data supports the research conclusion that in 2003 more people are choosing where to live based on how close they will be to their work.