Question

*Be sure to show work that supports your answers. *Include appropriate units in your answers.

3. (10 points) Pass rates for Math 355 at ARC have been 61.5%. In an effort to improve pass rates in the course, faculty piloted a mastery-based learning model where course content was delivered in a lab through a computer program. Students could either voluntarily enroll in the pilot program or they could take one of the other traditional classes. Of the 120 students who enrolled in the mastery-based course, 80 passed the course.

a) What kind of sample was used?

b) What this a designed experiment or an observational study?

c) Is the variable “pass rate” quantitative or qualitative?

d) At the 5% level of significance, test the claim that the mastery-based program increases pass rates by doing each of the following:

1) State the null and alternate hypotheses.

2) Test the claim using the approach of your choice.

3) Explain how the results of your test either reject or fail to reject the null hypothesis.

4) Write a formal conclusion.

5) If your conclusion is erroneous, what type of error is it? Briefly explain.

Answer 1

Given that,
possibile chances (x)=80
sample size(n)=120
success rate ( p )= x/n = 0.6667
success probability,( po )=0.615
failure probability,( qo) = 0.385
null, Ho:p=0.615
alternate, H1: p>0.615
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.66667-0.615/(sqrt(0.236775)/120)
zo =1.1631
| zo | =1.1631
critical value
the value of |z α| at los 0.05% is 1.64
we got |zo| =1.163 & | z α | =1.64
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.16314 ) = 0.12239
hence value of p0.05 < 0.12239,here we do not reject Ho
ANSWERS
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a.
random sample is used
b.
Observational Studies
Consider someone on the busy street of a New York neighborhood asking random people that pass by how many pets they have,
then taking this data and using it to decide if there should be more pet food stores in that area
Experimental studies. Experimental studies are ones where researchers introduce an intervention and study the effects. Experimental studies are usually randomized, meaning the subjects are grouped by chance.
Randomized controlled trial (RCT): Eligible people are randomly assigned to one of two or more groups.
c.
the variable pass rate quantitative
1.
null, Ho:p=0.615
alternate, H1: p>0.615
2.
test statistic: 1.1631
critical value: 1.64
3.
decision: do not reject Ho
p-value: 0.12239
4.
we do not have enough evidence to support the claim that the mastery-based program increases pass rates
5.
Type 2 error is possible when its fails to reject the null hypothesis.