STAT 2912: Statistical tests
Solution week 3
1. The following data gives the stroke index for 10 patients before and after treatment.
We wish to test the hypothesis that the treatment has no eect .
Before
After
109 57 53 57 68 72 51 65 52 61
56 44 55 40 6
STAT2912: Statistical Tests
Semester 2
Statistical Tests (Advanced)
2008
Tutorial week 12
1. A research paper reported the sizes of 120 groups of borers. The groups sizes were:
Group size: 0
Frequency: 24
1
16
2
16
3
18
4
15
56789
96534
10
3
11
0
12
1
Doe
STAT2912: Statistical Tests
Semester 2
Statistical Tests (Advanced)
2008
Exercise 12 Solutions
1. Under the Poisson model P (X = j ) = e j /j !, where X is the group size. We have
120 observations so estimate by the sample average x = 380/120 = 3.17.
The
STAT2912 Computer Lab 6 Solutions
Longen Lan 440351423
September 2, 2015
1
Comparing Multiple Samples
Today, we conduct statistical tests on multiple samples, specifically in this case, the result of multiple drugs
targeting at relieving itching.
1. This
STAT2912 Computer Lab 3 Solutions
Longen Lan 440351423
August 12, 2015
1
Sign Test and Wilcoxon Sign Rank Test
1. Today we use the data in amp which we analysed in Week 1 using t-tests.
(a) We first conduct the sign test on the data set.
i. Let dj denote
STAT2912 Computer Lab 11 Solutions
Longen Lan 440351423
October 14, 2015
1
Kernel Smoothing and Testing Goodness of Fit
Today, we consider the data frame ethanol, which contains information on E and N Ox from an experiment
where ethanol was burned in a si
STAT2912 Computer Lab 10 Solutions
Longen Lan 440351423
October 7, 2015
1
Further Regression and its Confidence Intervals
Today, we consider the data frame fuel.frame, which has information on makes of cars taken from the April
1990 issue of Consumer Repo
STAT2912 Computer Lab 9 Solutions
Longen Lan 440351423
October 7, 2015
1
Standard Linear Regression
Today, we consider the data frame fuel.frame, which has information on makes of cars taken from the April
1990 issue of Consumer Reports.
1. We want to ana
STAT2912 Computer Lab 12 Solutions
Longen Lan 440351423
October 21, 2015
1
Goodness of Fit Tests
Today, we perform 2 goodness of fit tests.
1. A die is rolled 60 times and the number of times each face appears are recorded.
(a) We want to test the fairnes
STAT2912 Computer Lab 3 Solutions
Longen Lan 440351423
August 12, 2015
1
Sign Test and Wilcoxon Sign Rank Test
1. Today we use the data in amp which we analysed in Week 1 using t-tests.
(a) We first conduct the sign test on the data set.
i. Let dj denote
STAT2912 Computer Lab 7 Solutions
Longen Lan 440351423
September 9, 2015
1
Additive Decomposition
Today, we explore additive decomposition by mean and median polishing by using data regarding the fuel
economy by 3 different types of automobiles among 6 di
STAT2912 Computer Lab 8 Solutions
Longen Lan 440351423
September 16, 2015
1
Two-Way ANOVA
Today, we conduct a two-way ANOVA test on data to determine whether the frequency that a super market
product is promoted at a discount affect the price that custome
STAT2912 Computer Lab 6 Solutions
Longen Lan 440351423
September 2, 2015
1
Comparing Multiple Populations
Today, we conduct statistical tests on multiple populations, specifically in this case, the result of multiple drugs
targeting at relieving itching.
The University of Sydney
The School of Mathematics and Statistics
Assignment 1 Solutions
Longen Lan 440351423
STAT2912: Statistical Tests (Advanced)
Semester 2, 2015
Lecturer: Qiying Wang
1. A plant manager, in deciding whether to purchase a machine of de
STAT2912: Statistical Tests
Semester 2
Statistical Tests (Advanced)
2008
Exercise 11 Solutions
1. Test H0 : = 0.5 vs H1 : > 0.5. Use Fishers Z transformation. The approximate
p-value for the test is
p = P (Z (tanh1 (0.73) tanh1 (0.5)/(1/ 6)
= P (Z 0.9294)
STAT2912: Statistical Tests
Semester 2
Statistical Tests (Advanced)
2008
Tutorial week 11
1. In a study of the relationship between the death rate from lung cancer and the per
capita consumption of cigarettes twenty years earlier, data from 9 countries yi
STAT2912: Statistical Tests
Solution week 4
1. The research department of a company that produces industrial string proposes a new
technique for strengthening the string and making it able to withstand stronger forces.
To nd out whether the new technique
STAT 2912: Statistical Tests
Solution week 5
1. An experimenter was convinced that his measuring equipment possessed variability,
which resulted in a standard deviation of 2. Sixteen measurements resulted in a sample
variance 6.1. Do the data disagree wit
STAT2912: Statistical Tests
Solution week 11
1. A study was constructed to determine whether a linear relationship exists between
the age (x) and the diameter (y in inches) at 1.5 meters level of chestnut trees. Ten
randomly selected chestnut trees were e
STAT2912: Statistical Tests
Solution week 12
1. A behavioural biologist believes that performance of a laboratory rat on an intelligence
test depends, to a large extent, on the amount of protein in the rats daily diet. To
check out the theory, he accumula
STAT2912: Statistical Tests
Solution week 13
1. 103 children attending a pre-school were classied by parents income group and by IQ
(intelligence quotient).
Income group
A
B
C
High IQ Moderate/low IQ
14
18
25
8
23
15
Do these data suggest that the fractio
STAT2912: Statistical Tests
Semester 2
Statistical Tests (Advanced)
2008
Tutorial week 5
1. The closing prices of two common stocks were recorded for a period of 16 days. The
means and variances were
y1 = 40.33
s2 = 1.54
1
y2 = 42.54
s2 = 2.96
2
Do these
STAT2912: Statistical Tests
Semester 2
Statistical Tests (Advanced)
2008
Exercise 5 Solutions
1. The hypothesis to be tested is
2
2
H0 : 2 = 1
2
2
vs H1 : 2 = 1 .
2
2
We use the test statistic: F = S2 /S1 . The observed value of the test statistic is give
STAT2912: Statistical Tests
Semester 2
Statistical Tests (Advanced)
2008
Tutorial week 6
1. An experiment was conducted to examine the eect of age on heartbeat rate when a
subject is subjected to a specic amount of exercise. Male subjects were selected at
STAT2912: Statistical Tests
Semester 2
Statistical Tests (Advanced)
2008
Exercise 6 Solutions
1. (a) Let j , j = 1, 2, 3, 4, denote the mean increase in heartbeats per minute for the
groups 10-19, 20-39, 40-59 and 60-69 respectively. The hypothesis to be
STAT2912: Statistical Tests
Semester 2
Statistical Tests (Advanced)
2007
Tutorial week 7
1. An experiment to compare the retention of two dierent forms of iron was performed
as follows: 108 subjects were randomly divided into 6 groups of 18 each. 3 groups