Question

Short term classes: Does taking a class in a short-term format (8 weeks instead of 16 weeks) increase a student’s likelihood of passing the course? For a particular course, the pass rate for the 16-week format is 59%. A team of faculty examine student data from 40 randomly selected accelerated classes and determine that the pass rate is 78%. Which of the following are the appropriate null and alternative hypotheses for this research question? Group of answer choices(A) H0: p = 0.59; Ha: p ≠ 0.59(B) H0: p = 0.59; Ha: p > 0.59(C) H0: p = 0.78; Ha: p ≠ 0.78(D) H0: p = 0.78; Ha: p > 0.59

Answer 1

C) is the most appropriate.

Explanation:

The pass rate for the 16-week format was obtained for only one particular course, whereas the pass rate for the 8-week format was obtained by examining 40 randomly selected, so
`H_0` should be

`H_0`:“The pass rate is p=0.78”

and

`H_a`: ““The pass rate is p<0.78”

But, from among the possible answers of choice, C) is the most suitable.

`H_0`:“The pass rate is p=0.78”

and

`H_a`: ““The pass rate is p≠0.78”

Answer 2

The null and alternative hypothesis should be:

`H_0: \pi=0.59\\\\H_a: \pi>0.59`

(Option B)

Explanation:

We have to determine the hypothesis accordingly to the claim we want to test.

In this case, we claim that taking a class in short-term format increase a student's likelihood of passing the course.

The null hypothesis is then that the likelihood stays the same, that is equal to 59% (the long-term likelihood of passing).

The alternative hypothesis, that is our claim based on the sample result (p=78%), is that the likelihood is bigger than 59%.

Then we can write:

`H_0: \pi=0.59\\\\H_a: \pi>0.59`