Question

Identifying Tests
For the following prompts include:
- the name of the test
- the parameter being tested, H0 and Ha.
Example: What test would you use to determine whether the starting salaries
for statisticians are greater than $80,000?
Ans: One-sample t-test for population mean, H0 : µ = $80, 000 vs. Ha : µ >
$80,000.

a. ) The 2010 Census found that the average family size in Minnesota was 3.05.
What statistical procedure would you use to test whether the average family
size in Minnesota is greater than 3.05 in 2019?

b. ) According to the 2017 American Community Survey, 5.7% of all workers in
Minneapolis/St. Paul urbanized area commute to work by public transportation. What statistical procedure would you use to test whether the proportion
of workers in Minneapolis/St. Paul urbanized area commute to work by public
transportation in 2019 has changed from than in 2015?

c. ) According to the 2017 American Community Survey, 4.3% of all workers in
Minneapolis/St. Paul urbanized area work in construction. What statistical
procedure would you use to test whether the proportion of the workforce in the
Minneapolis/St. Paul urbanized area is less than in 2017?

d. ) In 2016-2017 NBA season, the average salary per team was $97.6 million.
What statistical procedure would you use to test whether the average salary of
teams in the NBA in the 2019-2020 season is the same as in 2016-2017 season?

Answer 1

a)

Assuming we do not know the population standard deviation of family size in Minnesota.

One-sample t-test for population mean, H0 : µ = 3.05 vs. Ha : µ > 3.05

b)

One-sample z-test for population mean, H0 : p = 0.057 vs. Ha : p 0.057

c)

One-sample z-test for population mean, H0 : p = 0.043 vs. Ha : p < 0.043

d)

Assuming we do not know the population standard deviation of salary per team.

One-sample t-test for population mean, H0 : µ = $97.6 million vs. Ha : µ $97.6 million