Download Sampling Distribution Models

Based on past experience, a bank believes that 7% of the
people who receive loans will not make payments on time.
The bank has recently approved 200 loans.
A) What are the mean and standard deviation for the
sampling distribution of the proportion of clients in this
group who may not make timely payments?
B) What assumptions underlie your model? Are the
conditions met? Explain.
C) What’s the probability that over 10% of these clients will
not make timely payments?
Sampling Distribution
Models
CHAPTER 18 PART 3
Sampling Distribution Models
Don’t confuse the sampling distribution with the
distribution of the sample.
Watch out for skewed populations. The CLT assures
us that we can use the Normal model for the
sampling distributions, but the sample sizes will need
to be larger if the population is skewed. A rule of
thumb is to have sample size of at least 30.
We use the sample size to determine the standard deviation
for the sampling distribution. Since n is in the denominator of
the formula, the bigger the n, the smaller the standard
deviation.
HW 12 Problem 2: In a large class of introductory Statistics, the professor has each
person toss a coin 16 times and calculate the proportion of tosses that were heads.
The students report their results, and the professor plots a histogram of these several
proportions.
a) What shape would you expect the histogram to be? Why?
Symmetric. The sample size is small, but it is equally probable to get heads as it is to get tails.
b) Where do you expect the histogram to be centered?
0.5 because that is the probability of flipping a coin and landing on heads
c) How much variability would you expect among these proportions?
𝜎𝑝 =
𝑝𝑞
=
𝑛
.5(.5)
= 0.125
16
d) Explain why a Normal model should not be used here.
It does not meet the conditions since np = .5(16) = 8 and therefore np < 10.
Example: In a large class of introductory Statistics, the professor has each person toss a
coin 26 times and calculate the proportion of tosses that were heads.
a) Describe the sampling distribution using the 68-95-99.7 Rule.
Mean = 0.5, SD ≈ 0.1; 68% of sampling proportions are expected to be between 0.4 and 0.6;
95% are expected to be between 0.3 and 0.7; 99.7% are expected to be between 0.2 and 0.8
b) Confirm that you can use a Normal model here.
np = 13, nq = 13, and coin flips are independent
c) The number of tosses is increased to 64. Draw and label the sampling distribution
model.
N(0.5, 0.0625)
d) Explain how the sampling distribution changes as the number of tosses increases.
As n increases, the standard deviation decreases. The distribution will still be symmetric, but
less spread out (taller and more narrow).
Homework 11, 12, 13 & 14 is due by Friday.
No Quiz this week, there will be a chapter 18/19
quiz next Friday, March 10.
All quizzes must be completed prior to Spring
Break. Make arrangements if you plan on being
absent.