Practice Exam 2
STAT 319, Fall 2014
Instructor: Youngjoo Cho
Please print your name below:
Student Name: _
1
Date: _
1. Suppose that X1 , . . . , Xn is a random sample from pdf
f (x; ) = x1
0x1 0<
(a) Find MLE of .
L() =
n
Y
x1
= n
i
i=1
n
Y
x1
i
i=1
l()
Homework 8 Solution
Youngjoo Cho
1. (a) Let 1 and 2 be population means of lifetime on Duracell battery and
Eveready battery.
Y ) = 1 2
E(X
Y ) = 1.8/100 + 2.0/100 = 3.8/100
V (X
(b)
1. Parameter of interest : 1 2 .
2. Null and alternative hypothesis :
STAT 319 Homework 8
Due on November 21 before class starts
November 14, 2014
1. An article in the November 1983 Consumer Reports compared various types
of batteries. The average lifetimes of Duracell Alkaline AA batteries and
Eveready Energizer Alkaline A
Homework 7 solution
Youngjoo Cho
9.1.2 b : Space generated by alternative hypothesis should not be intersected with
one generated by null hypothesis.
c : Null hypothesis should have equality.
d,f : Alternative hypothesis should be based on null value.
e :
HW 1 solution
Youngjoo Cho
September 17, 2014
1. The probability that a grader will make a marking error on any particular
question of a multiple-choice exam is 0.2. There are ten questions and questions
are marked independently.
(a) What is probability t
Practice Exam 1
STAT 319, Fall 2014
Instructor: Youngjoo Cho
Please print your name below:
Student Name: _
1
Date: _
1. Let X1 , . . . Xn be a random sample from Bernoulli(p). The pdf of Bernoulli(p) is
P (X = x) = px (1 p)1x
x = 0, 1
(a) Find method of m
Homework 5 solution
Youngjoo Cho
8.1.1 (a) By table, 99.5%
(b) By table, 85%
(c) P (Z z/2 ) = 0.9985. Hence by table, 2.97 (or 2.96)
(d) P (Z z/2 ) = 0.875 By table, 1.15.
8.1.3 (a) Narrower, because z/2 decreases when increases.
(b) Incorrect. There is n
HW 3 solution
Youngjoo Cho
6.2.13(First edition) (a)
50
49.75
50
X
50.25
50
50.25) = P
P (49.75 X
1/ 100
1/ 100
1/ 100
P (2.5 Z 2.5) = P (Z 2.5) P (Z 2.5) = 0.9876
(b)
49.8
49.75
49.8
X
50.25
49.8
50.25) = P
P (49.75 X
1/ 100
1/ 100
1/ 100
P (0.5
Homework 4
Due date : Oct 1 before class starts
(1) From textbook: 7.2.21(a,b),7.2.23, 7.2.30
7.2.21 (a) Since we have binomial random variable,
n x
f (x; p) =
p (1 p)nx
x
Then the likelihood function is
n
l(p) = log
+ xlogp + (n x)log(1 p)
x
d
x nx
x
Stat 319 Midterm
Chapters 6, 7, 8
Wednesday, February 27th 2008
Before opening the paper:
Write your name, PSU ID # and sign at the space provided below:
NAME : _
PSU ID # : _
SIGNATURE : _
Grade:
Problem 1:
out of 25
Problem 2:
out of 30
Problem 3:
out o
1
Inference based on one sample - Confidence Interval and Hypothesis Testing
1. Inference about the population mean
(a) Normal population with known variance.
+ Z/2
Z/2 , X
i. (1 )100% confidence interval for : X
n
n
Z
ii. (1 )100% lower bound for :
Midterm 1 - 02/26/2016
Name:
PSU ID:
Problem 1:
Problem 2:
Problem 3:
Problem 4:
Problem 5:
Bonus points
Total:
out of 20
out of 5
out of 39
out of 26
out of 10
out of 100
1. This test consists of 8 pages. Check that you have all pages. The tables are pro
Homework 10 Solution
Youngjoo Cho
1. (a) By looking at this scatterplot below, we can see that there is positive
relationship between daughters height and midparents height.
(b) Note that n = 11.
n
X
(xi x)(yi y) = 51.77273
i=1
n
X
i=1
1
(xi x)2 = 54.1818
Homework 5 solution
Youngjoo Cho
is used.
7.1.3 (a) 1.348 , X
can be used.
(b) 1.348, Since normal distribution is assumed, X
(c) By using empirical rule, we can use
+ z0.9
, where
= X,
is samq P
2 . Note that z0.9 = 1.28.
ple standard deviati
Homework 2 Solutions 6.50. We know that if U = (n 1)S 2 / 2 2 , then E(U ) = n 1 and V (U ) = 2(n 1). Using n1 Equation (6.12) with X = U , k = 1/2, and = n 1 we get E( U ) = 2(n/2)/[(n 1)/2]. a. E(S 2 ) = E[ 2 U/(n 1)] = 2 E(U )/(n 1) =
Homework 3 Solutions 7.4. a. X Y is an unbiased estimator for 1 2 since E(X Y ) = 1 2 . To see this, E(X Y ) = E(X) E(Y ) = 1 m
m
E(Xi )
i=1
1 n
n
E(Yi ) = 1 2
i=1
For the observed data, the estimate of 1 2 is x y = 121.44 113.80 = 7.
In an experiment, with n=13 observations, the estimated regression line is y=0.365+ 0.967x. I am giving you the following MSE=0.0373 and MSR=1.0427. a) Calculate SSE. b) Calculate the estimated variance of the regression c) Calculate the Coefficient
Homework 7
Due date : Nov 12 before class starts
9.1.2, 9.1.8, 9.1.11, 9.2.15, 9.2.17, 9.2.31, 9.3.38
Additional Note : For 9.2.31, do analysis both by hand and
Minitab. Attach Minitab output in the homework and calculate
p-value by using Minitab.
STAT 319 Homework 10
Due by Dec 12 before class starts
1. As an alternative to the use of fathers height to predict sons height, Galton
also used the mid-parent height, the average of the fathers and mothers
heights. Here are the nights of 11 female stude
STAT 319 Homework 9
Due on Dec 8 before class starts
December 3, 2014
1. An experiment to compare I = 5 brands of golf balls involved using a robotic
driver to hit J = 7 balls of each brand. The resulting between-sample
and within-sample estimates of 2 we
Homework 4
Due date : Oct 1 before class starts
(1) From textbook: 7.2.21(a,b),7.2.23, 7.2.30
(2) From outside of textbook:
1. Let X1 , . . . , Xn be a random sample from a Gamma(, ) distribution.
Note that the pdf of Gamma(, ) is
f (x; , ) =
1
()
x1 ex/
STAT 319 Homework 1
Due Sep 10 before class starts
1. The probability that a grader will make a marking error on any particular question
of a multiple-choice exam is 0.2. There are ten questions and questions are marked
independently.
(a) What is probabil
Midterm 1 - 10/06/2017
Name:
PSU ID:
Problem 1:
Problem 2:
Problem 3:
Problem 4:
Problem 5:
Problem 6:
Bonus points
Total:
out of 12
out of 15
out of 9
out of 12
out of 12
out of 40
out of 100
1. This test consists of 8 pages. Check that you have all page