Question

part 1.
An independent measures study has df = 48. How many total participants were in the study?
a. 24
b. 46
c. 50
d. There is not enough information

part 2.

A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes.

A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time. If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school busses to help shorten commute time. What would a Type 2 error mean in this context?

a. The local government decides that the average commute time is 30 minutes.

b. The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact 30 minutes.

c. The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes.

d. The local government decides that the data do not provide convincing evidence of an average commute time different than 30 minutes, when the true average commute time is in fact 30 minutes.

Answer 1

Answer part 1

we know that the degree of freedom for independent measures is given as (n1+n2)-2

where n1+n2 represents the total number of participants in the study.

it is given that degree of freedom = 48

So, we can write it as

48 = (n1+n2)-2

adding 2 on both sides, we get

48+2 = (n1+n2) - 2 +2

this gives us

(n1+n2) = 50

So, option C is correct answer

Part 2

we know that the type II error is defined as failure of rejecting a false null hypothesis, i.e. failing to reject a false null hypothesis.

In the given question, a local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time.

So, we assume that null hypothesis is that the "average commute time is 30 minutes."

and alternate hypothesis will be the research question, i.e. alternate hypothesis will be that "average commute time is higher than 30 minutes."

So, type II error in this case will be that the average commute time is 30 minutes, when in actual the average commute time is higher than 30 minutes

Option C is correct answer