Question

1. 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? 1

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.

we will use one sample t test

Null and Alternative hypothesis:

Ho : µ = 3.05

H1 : µ > 3.05

--

b) One-sample z-test for population proportion

Null and Alternative hypothesis:

Ho : p = 0.057

H1 : p ≠ 0.057

--

c) One-sample z-test for population proportion

Null and Alternative hypothesis:

Ho : p = 0.043

H1 : p < 0.043

--

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

we will use one sample t test

Null and Alternative hypothesis:

Ho : µ = 97.6

H1 : µ ≠ 97.6