[1]
ii.Based on this plot, the required condition does not appear to be met. However you can assure Harry that the interval estimate is still valid. Why is that the case? Explain briefly:

4.
Coronary bypass surgery
is a procedure used to reduce the risk of death from
coronary artery disease.
A random
sample of 60
patients who had emergency
bypass surgery and an independent random sample of 100 patients who had
non-emergency surgery were obtained.
Patients were classified according to
whether they survived the surgery.
The results are shown below:
Survived?
Surgery Type
Yes
No
Total
1 =
Emergency
48
12
60
2 =
Non-emergency
88
12
100
a.
A medical researcher wants to determine if the proportion that survive
emergency surgeries is significantly less than the proportion that survive non-
emergency surgeries at the 5% level.
Let
p
1
represent the population
proportion of all emergency surgeries that result in survival, and
p
2
represent
the population proportion of all non-emergency surgeries that result in
survival.
State the hypothesis to be tested:
[2]
H
0
: __________________________
H
a
: __________________________
b.
Under the null hypothesis, the two population proportions are the same.
Compute the estimate of this common population proportion.
Show all work.
[2]
Final answer: _______________
c.
Compute the test statistic for testing the hypotheses in part (a).
Show all work.
[2]
Final answer: _______________
d.
Report the
p
-value corresponding to the hypotheses in part (a) and your test
statistic in part (c). Show your work.
[2]
Final answer: _______________
e.
At the 5% level, do the data provide sufficient evidence
to say the population
survival rate of emergency surgeries is less than the population survival rate of
non-emergency surgeries?
[2] Circle one:
Yes
No
197

f.
If there is no difference between the two population survival rates, and we
were to repeat this study many, many times, each time conducting the same
hypothesis test at the same significance level, then we would expect to reject
H
0
…
(circle one)
[2] ...
about 95% of the time.
... about 5% of the time.
Cannot be determined.
5. Does it make sense? Decide whether each statement is true or false.
6.
Which Technique? –
For each scenario below, determine if the most
appropriate statistical analysis technique is conducting a hypothesis test (HT)
or constructing a confidence interval (CI).
Then also give the symbol for the
corresponding parameter that is of interest.
[2 points each]
a.
A fitness instructor is working on a project which involved having a random
sample of HS students participate in a fitness course during their last semester
in HS.
For each student it was determined whether or not their fitness level
improved.
The instructor would like to assess if the improvement rate for all
male students is higher than that for all female students.

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- Fall '10
- Gunderson
- Statistics, Statistical hypothesis testing, researcher