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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.
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STAT 205 Name:______________________________ Fall 2007 Exam 2
P{Y = j} = (^) n Cj p j^ (1 – p) n-j
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 Y − Y ± 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.
State the definition of a P-value.
For a 95% confidence interval for the population mean, μ, how is the length of the interval related to margin of error?
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}.
(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.
(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.
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).
