Question 628068: A recent research report (Behenam & Pooya, 2006)
began, “There is probably no other area of health care
that requires a cooperation to the extent that orthodontics
does,” and explored factors that affected the
number of hours per day that patients wore their orthodontic
appliances. The patients in the study reported
that they used their appliances, on average,
14.78 hours per day, with a standard deviation of 5.31.
We’ll treat this group as the population for the purposes
of this example. Let’s say a researcher wanted
to study whether a DVD with information about orthodontics
led to an increase in the amount of time
patients wear their appliances but decided to use a
two-tailed test to be conservative. Let’s say he studied
the next 15 patients at his clinic, asked them to
watch the DVD, and then found that they wore their
appliances, on average, 17 hours per day.
a. What is the independent variable? What is the dependent
variable?
b. Did the researcher use random selection to choose
his sample? Explain your answer.
c. Conduct all six steps of hypothesis testing. Be sure
to label all six steps.
d. If the researcher’s decision in step 6 was wrong,
what type of error would he have made? Explain
your answer.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The patients in the study reported
that they used their appliances, on average,
14.78 hours per day, with a standard deviation of 5.31.
We’ll treat this group as the population for the purposes
of this example. Let’s say a researcher wanted
to study whether a DVD with information about orthodontics
led to an increase in the amount of time
patients wear their appliances but decided to use a
two-tailed test to be conservative. Let’s say he studied
the next 15 patients at his clinic, asked them to
watch the DVD, and then found that they wore their
appliances, on average, 17 hours per day.
a. What is the independent variable?
What is the dependent variable?
b. Did the researcher use random selection to choose
his sample? Explain your answer. No: his sample was
based on convenience.
------------------------
c. Conduct all six steps of hypothesis testing. Be sure
to label all six steps.
Ho: u = 14.78 hrs
Ha: u # 14.78
---
t(17) = (17-14.78)/[5.31/sqrt(17)] =1.7238
---
p-value = 2*P(t > 1.7238 when df = 14) = 2*tcdf(1.7238,100,14) = 0.1067
----
Since the p-value is greater than 5%, fail to reject Ho at the 5%
significance level.
-----
d. If the researcher’s decision in step 6 was wrong,
what type of error would he have made? Explain
your answer.
---
Ans: Type II. He would conclude the DVD had had a significant effect
when, in fact, it had not.
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Cheers,
Stan H.
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