3. According to the U.S. department of transportation, there is a mean of 1.97 vehicles per

household in the U.S with a standard deviation of 0.35 (population parameters). A transportation

researcher has hypothesized that people with a college degree (or higher) in environmental

sciences are less likely to drive a car than people without higher education degrees in

environmental sciences because they tend to be more environmentally conscious. Using a

random sample of 650 people in the U.S. with a degree in environmental sciences, the researcher

found that the mean number of vehicles per household was 1.69 with a standard deviation of

0.18. Perform a hypothesis test to determine whether there is a difference between the mean

number of vehicles owned by all Americans, and the mean number of vehicles owned by people

with a college degree or higher in environmental sciences.

(hint: this is the first of three types of hypothesis testing, a population with known parameters

vs. a specific group. Use a Z-distribution)

[35 points]

a.

What assumptions must you make when performing a hypothesis test to compare a

sample mean to a population mean? (Three assumptions). And, what do these

assumptions tell us (in other words, why make these assumptions)?

b.

Fill in the values for the following variables:

=

=

X =

N =

c.

State your research and null hypotheses using a

one-tailed test

(note that the researcher

has a theoretical reason for using a one-tailed test).

d.

Using = 0.05 (a 95% confidence level)

compute the test statistic

using a Z-distribution

(as our population standard deviation is known).

e.

What can you conclude about your hypothesis (reject or fail to reject the null)? Interpret

your result in two sentences. Make sure to refer to the specific units of the variable AND

the specific population.