Download handout14 - Penn Math

STAT111-(205,206,208)
Kwonsang Lee
Week 14 (April 24, 2015)
Note:
• Today is the last mandatory recitation to attend.
• Review session: next Friday(5/1) in the same classroom at the same time.
• My last office hour: Next Tuesday(4/28) 1-2pm and Wednesday(4/29) 3-4pm
• Professor’s office hour: May 4th, 3-5pm
• I’ll prepare a box to return Homework 6 and 7 in the statistic department (4th floor, JMHH).
I’ll send you an email when the box is prepared.
Example: Time magazine reported the result of a telephone poll of 800 adult Americans. The
question posed of the Americans who were surveyed was: “Should the federal tax on cigarettes be
raised to pay for health care reform?” The results of the survey were:
Non-Smokers
n1 = 605
y1 = 351 said “yes”
351
p̂1 = 605
= 0.58
Smokers
n2 = 195
y2 = 41 said “yes”
41
p̂2 = 195
= 0.21
a. Compute the 95% confidence interval for p1 − p2 .
b. Test whether the two populations - smokers and non-smokers - differ significantly with respect
to their opinions.
Some past final exam problems: Warren Ewens, 2014 Fall Final Exam
Question 1. A coin with probability 0.7 for head on each flip was flipped five times, and you are
told that there were at least three heads. What is the probability that all five flips gave heads?
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Question 2. The height of a randomly chosen male is a random variable having a normal distribution with mean 69 and standard deviation 3 (All measurements in this question are in inches). The
height of a randomly chosen female is a random variable having a normal distribution with mean
67 and standard deviation 4. Find the probability that the average height of four randomly chosen
males exceeds average height of four randomly chosen females.
Question 3. Suppose that the height of an adult female taken at random has a normal distribution
with mean 66 and standard deviation 4. You are told that the probability that the average height
of n adult females taken at random exceeds 66.329 inches is 0.05. What is the value of n?
Check definitions or concepts that you think you know: e.g.
P-value
hypothesis test and
Question 4. Outline the steps used in hypothesis testing using the “critical value” approach.
Indicate the changes made to this approach if we wish to operate via a P-value.
Question 5. Give a precise definition of a P-value. Indicate, giving reasons for your answer,
whether a sufficiently large or a sufficiently small P-value leads you to reject a null hypothesis.
Large or small compared to what? Does your answer change if we consider a two-sided test instead
of a one-sided test? Use your discussion to indicate why the P-value in a two-sided test is calculated
as the sum of two probabilities.
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