1.7
Exercises
1.7 Exercises lg
For Further Reading
The American Statistical Association series What is a Survey? provides an intro-
duction to survey sampling, with examples of many of the concepts discussed in
Chapter 1. In particular, see the chapter Ju
Assignment #4
Ngan Nguyen
7.14
a. X = number of years of education for self-employed individuals
in the United States
b. x ~N(13.6,
3.0
) = N(13.6, .3)
100
The mean of the sampling distribution of years of education for a
random sample of size 100 is 13.
#Run the following code line by line.
NoU<-read.delim("http:/stat.umn.edu/~bkuzmak/data/Getting2NoUS2016.txt",header
= T)
attach(NoU)
boxplot(physical.exercise~live.on.campus, outline= F, xlab="live on campus",
ylab = "time spent exercising")
PEon=physica
4.8 Exercises
155
Ratio estimator: An estimator of the population mean or total based on a ratio with
an auxiliary quantity for which the population mean or total is known.
Regression estimator: An estimator of the population mean or total based on a
regr
Chapter 7
Visualizing a Sampling Distribution
Lets review what we have learned about sampling distributions. We have considered sampling
distributions for the test of means (test statistic is U) and the sum of ranks test (test statistic is
R1 ). We have l
Chapter 9
Statistical Power
9.1 Type 2 Errors and Power
Table 9.1 is a reproduction of Table 8.8 in Section 8.3 that presented the ideas of Type 1 and Type 2
errors. In Chapter 8 we focused on the rst column of this table, the column which states that the
Chapter 10
Populations: Getting Started
You have now completed Part 1 of these notes, consisting of nine chapters. What have you learned?
On the one hand, you could say that you have learned many things about the discipline of Statistics.
I am quite sure
Chapter 11
Bernoulli Trials
11.1 The Binomial Distribution
In the previous chapter, we learned about i.i.d. trials. Recall that there are three ways we can have
i.i.d. trials:
1. Our units are trials and we have decided to assume that they are i.i.d.
2. W
Chapter 12
Inference for a Binomial p
In Part 1 of these Course Notes you learned a great deal about statistical tests of hypotheses.
These tests explore the unknowable; in particular, whether or not the Skeptics Argument is true.
In Section 11.4, I briey
Chapter 13
The Poisson Distribution
Jeanne Antoinette Poisson (17211764), Marquise de Pompadour, was a member of the French
court and was the ofcial chief mistress of Louis XV from 1745 until her death. The pompadour
hairstyle was named for her. In additi
Chapter 14
Rules for Means and Variances; Prediction
14.1 Rules for Means and Variances
The result in this section is very technical and algebraic. And dry. But it is useful for understanding
many of prediction results we obtain in this course, beginning
Chapter 15
Comparing Two Binomial Populations
In this chapter and the next, our data are presented in a 2 2 contingency table. As you will learn,
however, not all 2 2 contingency tables are analyzed the same way. I begin with an introductory
section.
15.1
#lab 8 part c
#Do a simulation with 1 sample. We will get 1 "phat" in this case.
set.seed(1)
x=sum(rbinom(83,1,p=0.2)
(phat=x/83)
#Do a simulation with 100 sample. We will get 100 "phat"s in this case.
p.hat=NULL
set.seed(1)
for(i in 1:100)cfw_
x=sum(rbin
Ngan Nguyen
Assignment #2
1.
a. Sample space S =cfw_Clinton, Sanders, OMalley
b. R delegate from a rural region
B delegate support Bernie Sanders
c. P(R) = 946/1660 = 0.569
d. Rc means the delegates who are not from a rural region.
P(Rc) = 1- P(R) = 1- 0.
Ngan Nguyen
Homework #3
6.10
a.
Let X = the profit of the farmer. X has the values of $80,000, $50,000 and
$20,000. And the probabilities are 0.7, 0.2, and 0.1 respectively.
x
80000
50000
20000
p(x)
0.7
0.2
0.1
b.
P(X 50000) = P(X=50000) + P(X=20000)
= 0.
Ngan Nguyen
Assignment #6
9.2
a. An alternative hypothesis because the parameter in this statement falls in
alternative range of values.
b. A null hypothesis because the parameter in this statement takes a
particular value.
c. An alternative hypothesis be
Ngan Nguyen
Assignment 10
11.10
a. Null hypothesis Ho: the variables marital happiness and family income
are independent
Alternative hypothesis Ha: the variables marital happiness and family
income are dependent
b. df = (r-1)(c-1)= (3-1)(3-1) = 4
2 = 9.4
NGAN NGUYEN
Assignment #5
8.2
8.24
a. point estimate = 0.548
b. interval estimate = (0.548-0.03, 0.548+0.03) =(0.518, 0.578)
c. The difference is that there a point to estimate for the point estimate, but
there is a range for interval to estimate.
a. p^=6
Assignment #1
1.16
a. I would find more surprising when flipping the coin 500 times and observing all
heads.
b. Because you observed the sequences of flipping coin by doing many times, the
sequences of flips tend to repeat. So the proportions of heads whe
Ngan Nguyen
Assignment 9
14.2
a. 1 : the interacting with a teller at the bank
2 : the using ATMs
3 : the using banks Internet banking service
Ho: 1 = 2 = 3
Ha: at least two of the population means are different
b. df 1 = 3-1=2
df 2 =400-2=397
F=3, the ri
Ngan Nguyen
Assignment#7
Problem:
1. One-sample z-test for population proportion
Ho: p=0.093
Ha: p > 0.093
2. One-sample t-Test for population mean
Ho: = 60
Ha: < 60
3. One-sample z-test for popul
Ngan Nguyen
Assignment #8
10.54
a. Assumption: random sample, the distribution of the paired difference is
approximately normal.
Hypotheses: Ho: ! = 0
Ha: ! 0
!
Test statistic: t=
! !
!
Chapter 17
Inference for One Numerical Population
In Chapter 10 you learned about nite populations. You learned about smart and dumb random
samples from a nite population. You learned that i.i.d. trials can be viewed as the outcomes of
a dumb random sampl