Transcript Problem 1

Problem 1
Suppose 40% of registered voters in a certain town are
Democrats. You take a simple random sample of 80
voters.
a) If your survey avoids biases, you expect __________
Democrats, give or take ____________ or so, in your
sample.
b) What is the probability that your sample actually
predicts a Republican victory?
Problem 2
A student doing a survey at a large university found
that her random sample of 160 students reported an
average GPA of 3.5 with a standard deviation of 0.45.
The registrar’s office published the average GPA to be
2.85. Can the difference be explained by sampling
variability? If not, how else can it be explained?
Problem 3
A simple random sample of size n =70 has a mean of 87
and a sample SD of 0.5.
a) Find a 98% confidence interval for the population
mean.
b) How important is it that we don’t know the shape
of the population?
Problem 4
The Motor Vehicle Department plans to estimate the
proportion of drivers who have not received any tickets
for moving violations during the past three years.
How large a sample of its records should it take to be
within 0.02 of the true proportion with 99%
confidence?
Problem 5
Consider the following matched-pair data set. Assume
normality of the parent populations. Find a 95%
confidence interval for the difference in means.
x: 7 9 9 6 8 8
y: 4 4 3 4 9 5
Problem 6
To determine the effectiveness of a certain vitamin
supplement, the weight increase for two groups of
mice was measured:
Control group:
12
Treatment group: 18
19
16
14
23
20
23
Test at the 5% level of significance whether the
vitamins treatment results in a higher weight gain.