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Statistics Exam 2 - Fall 2007 - Answers and Questions, Exams of Statistics

The second exam for stat 205 - introduction to probability and statistics, held in fall 2007. The exam covers various topics such as p-values, confidence intervals, hypothesis testing, and the distribution of sample means. Students are required to answer a series of questions related to these topics.

Typology: Exams

2012/2013

Uploaded on 02/26/2013

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STAT 205 Name:______________________________
Fall 2007
Exam 2
P{Y = j} = nCj pj (1 – p)n-j
Z =
n
Y
σ
µ
n
s
tY 2
α
±
t =
n
s
Y
µ
2
2
2
1
2
1
2
21 )( n
s
n
s
tYY +±
α
t =
2
2
2
1
2
1
21 0)(
n
s
n
s
YY
+
pf3
pf4
pf5

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STAT 205 Name:______________________________ Fall 2007 Exam 2

P{Y = j} = (^) n Cj p j^ (1 – p) n-j

Z =

n

Y σ

−μ

n

s Y t α 2 ±

t =

n

s

Y − μ

2

2 2 1

2 1 (^1 ) ( ) n

s n

s YY ± t α +

t = 2 2

2 1

( 1 2 ) 0

n

s n

s

Y Y

− −

Part I: Answer eight of the following nine questions. If you complete more than eight, I will grade only the first eight. Five points each.

  1. State the definition of a P-value.

  2. For a 95% confidence interval for the population mean, μ, how is the length of the interval related to margin of error?

  3. A certain drug causes drowsiness in 20% of patients. Suppose the drug is to be given to 5 randomly chosen patients. Let p ˆ^ represent the proportion of patients in the sample who

experience drowsiness. Find Pr{ p ˆ^ ≤ 1}.

  1. (Circle the correct answer) A study of the effect of transdermal estradiol on postmenopausal women was conducted. Plasma levels of plasminogen-activator inhibitor type 1 (PA-1) was measured for 20 women before and after being administered transdermal estradiol. We would use the independent / dependent (paired) samples method in order to conduct a test of hypothesis for the difference between the mean PA- levels of these two populations.

  2. (Circle the correct answer.) The power for a hypothesis test is

P{failing to reject H 0 |H 0 is false} P{rejecting H 0 | H 0 is false} Pr{rejecting H 0 | H 0 is true} Pr{failing to reject H 0 | H 0 is true}

Part II: Answer every part of the next two problems. Read each question carefully, and show your work for full credit.

  1. (25 pts) Androstenedione is a steroid that is thought by some athletes to improve strength. Researchers investigated this claim by giving Androstenedione to one group of men and a placebo to a control group of men. One of the variables measured in the experiment was the increase in “lat pull-down strength” in pounds of each subject after four weeks. (A lat pull-down is a type of weight lifting exercise.) The data is summarized in the following table. Andro Control n 10 9 mean 20 14. SD 12.5 13. Conduct a test of hypothesis at the 0.05 significance level to compare the two groups. Note, WS approximation gives 16.5 degrees of freedom. Please place your steps next to the appropriate number below.
  1. Certain types of nerve cells have the ability to regenerate a part of the cell that has been amputated. In an early study of this process, measurements were made on the nerves in the spinal cord of rhesus monkeys. Nerves emanating from the left side were cut, while nerves on the right side were kept intact. During the regeneration process, the content of creatine phosphate (CP), used as an indicator of muscular activity, was measured in the left and right portion of the spinal cord. The following table summarizes the data from this study.

Animal

Right side (Control)

Left side (Regenerating) Difference 1 16.3 11.5 4. 2 4.8 3.6 1. 3 10.9 12. 4 14.2 6.3 7. 5 16.3 15.2 1. 6 9.9 8.1 1. 7 29.2 16.6 12. 8 22.4 13.1 9. Mean 15.50 10.86 4. SD 7.61 4.49 4.

2a) (25 pts) Construct a 90% confidence interval for the difference in mean creatine phosphate levels for the two sides.

2b) (5 pts) Interpret the interval you computed in part (a).