Problem
Points
1
20
2
20
3
20
4
20
5
20
EC
10
Total
110
Name ________________________
Test #4
Math 150 / Fall 2012 / M. Zeitzew
Show all work. One page notes both sides & calculator allowed.
Don’t forget the rounding rules!!!
ASSUME ALL POPULATIONS ARE NORMALLY DISTRIBUTED AND
SIMPLE RANDOM SAMPLING IS DONE
Before
200 174 198 170 179 182 193 209 185 155 169 210
After
191 170 177 167 159 151 176 183 159 145 146 177
Difference
d= Before-After
1. Captopril is a drug designed to lower systolic blood pressure. When subjects were tested with
this drug, their systolic blood pressure readings (in mm Hg) were measured before and after drug
treatment, with the results given in the following table1. Use = 0.05 to test the claim that
Captopril is effective at lowering systolic blood pressure. Use the traditional method. (HINT:
these are dependent samples, so you’ll need statistics on the before/after differences)
a. State the hypotheses and identify the claim
H0:
H1:
b. Find the test statistic
1
Based on data from “Essential Hypertension: Effect of an Oral Inhibitor of Angiotensin-Converting Enzyme,” by
MacGregor, et al., British Medical Journal, Vol. 2
c. Find the critical value(s) (& draw a picture to illustrate test statistic and critical
value(s))
d. Make the decision (and explain why!)
e. Summarize the results
2. Among 13,200 submitted abstracts that were blindly evaluated (with authors and institutions not
identified), 26.7% were accepted for publication. Among 13,433 abstracts that were not blindly
evaluated, 29.0% were accepted2. Use a 0.01 significance level to test the claim that the
acceptance rate is the same with or without blinding. Use the P-Value method.
a. State the hypotheses and identify the claim
H0:
H1:
b. Find the test statistic
c. Find the critical value(s) (& draw a picture to illustrate test statistic and critical
value(s))
d. Make the decision (and explain why!)
2
Based on data from “Effect of Blinded Peer Review on Abstract Acceptance,” by Ross, et al., Journal of the American
Medical Association, Vol. 295, No. 14
3. A simple random sample of 80 workers with high school diplomas is obtained, and the annual
incomes have a mean of $37,622 and a standard deviation of $14,115. Another simple random
sample of 39 workers with bachelor’s degrees is obtained, and the annual incomes have a mean
of $77,689, with a standard deviation of $24,227. Use a 0.01 significance level to test the claim
that the two samples are from populations with the same standard deviation. Use the traditional
method
a. State the hypotheses and identify the claim
H0:
H1:
b. Find the test statistic
c. Find the critical value(s) (& draw a picture to illustrate test statistic and critical
value(s))
d. Make the decision (and explain why!)
4. Listed below are the numbers of deaths from lightning on the different days of the week. The
deaths were recorded for a recent period of 35 years3. Use a 0.01 significance level to test the
claim that deaths from lightning occur on the different days with the same frequency. Can you
provide an explanation for the result? Use the Traditional method.
Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Deaths
574
445
429
473
428
422
467
a. State the hypotheses and identify the claim
H0:
H1:
b. Find the test statistic
c. Find the critical value (& DRAW A PICTURE ILLUSTRATING TEST STATISTIC and
critical value)
d. Make the decision
e. Summarize the results
3
Based on data from the National Oceanic and Atmospheric Administration
5. Find the best predicted quality score of a Hitachi television with a price of $1900. Is the predicted
quality score close to the actual quality score of 56? Show your work or you will lose points.
Price
Quality
Score
2300 1800 2500 2700 2000 1700 1500 2700
74
73
70
66
63
62
52
68
EXTRA CREDIT
6. Listed below are actual high temperatures and the high temperatures forecast five days in
advance.
a. First compute the differences between the actual and forecast highs and add them to
the table.
b. Perform the hypothesis test below. Use a 0.05 significance level with the sign test to
test the claim that the population of differences has a median of zero.
c. What do the results suggest about the accuracy of the forecasts?
Actual High
Forecast
High 5 Days
Earlier
Difference
78
80
71
73
78
75
63
63
70
77
79
74
75
76
78
76
75
77
71
74
State the hypotheses and identify the claim
H0:
H1:
Find the test statistic
???
Make the decision
Summarize the results