Question

For each of the following situations write down whether a z-test is applicable, a t-test, a two-sample

z-test, or chi-square:

(a) To determine if it is true that 1% of tax payers in the US have an annual salary greater than

$343,927 we obtain a simple random sample of 10,000 US tax payers and find that 93 of them

have an annual salary greater than $343,927.

(b) The average height students at Stanford in 1891 was 70 inches with an unknown standard

deviation. We believe current students may be taller than the students in 1891 so we do a

simple random sample of 20 students this year.

(c) At the time of the 2008 election, a census of national voter registers had 33% Democrat, 32%

Other, 28% Republicans, 4% Green, and 3% Libertarian. A political scientist wants to know

if the composition of party affiliation in 2016 is different. To address this question a simple

random sample of 256 registered voters is conducted and party affiliation is assessed.

(d) Elon Musk wants to convince people that the new Tesla autopilot cars are safer than human

drivers. To test this hypothesis Tesla recruits 300 people and randomly assigns half to drive a

Tesla car without the aid of autopilot, the other half are allowed to use the autopilot feature.

After a year of driving, the researchers record whether each drive had zero incidences or at

least one incident.

Answer 1

(a)

In the given scenario, the researcher wants to check whether it is true that 1% of tax payers in the US have an annual salary greater than $343,927.
Here, the parameter of interest is true population proportion of tax payers that have an annual salary greater than $343,927.

Therefore, the appropriate statistical test is z-test for single proportion.

(b)

In the given scenario, the parameter of interest is true mean height students at Stanford in 1891. Here, the standard deviation is unknown.

Therefore, the appropriate statistical test is t-test for single mean.

(c)

In the given scenario, the researcher wants to check whether there is some association between the registered voter's party affiliation. Here the data is provided in the form of percentages.

Therefore, the appropriate statistical test is chi-square test of independence.

(d)

In the given scenario there are two variables-

First variable: Tesla cars which is divided into two levels, such as Tesla car without the aid of autopilot and Tesla car with the aid of autopilot.

Second variable: Incidence rate which is recorded at two levels such as, zero incidence and atleast one incident.

Therefore, the appropriate statistical test is chi-square test of independence.