Problem 5. Estimating means
Newly developed diet pills are known to work differently for men and for women. A sample of 120 subjects (50 males,
70 females) participated in this study, in which their pre- and post-treatment weights were measured:
Male (N=50)
Female (N=70)
Pre
Post
Diff (
m
)
Pre
Post
Diff (
x
207
202
-5
165
155
S
8
6
10
9
Our first goal is to test the claim that there is an effect of the diet pills for males.
Let
D
m
be the sample mean difference
for
males
, and
m
be the population parameter:
0
:
0
m
H
0
:
m
a
H
5.1
Is this a
paired sample
or
independent samples
test?
(circle one)
Set up the appropriate test statistic for this test.
(see soln sheet)
5.2
Formula for the test statistic:
5.3
With plug in values :
5.4
What is the distribution of this test
statistic?
Show the reference distn, df and whether to use
or
5.5
Is this is a 1 or 2 tailed test?
5.6
State the conclusion if the value of the
test statistic had been -6.71 for
=0.01.
Test the claim that effects of the diet pills are same for males and for females.
For these purposes, assume
you have been given the pre-post weight differences for each person (note: treat the difference Di as the
measured random variable).
5.7
State the null and alternative
hypotheses
f
)
-10
12
15
/2

Practice Final
Stat 311 Spring 2015
8
5.8
Is this test based on
paired sample
or
independent samples
?
(circle 1)
Using a pooled estimate, what is the formula for the standard error for the difference between the male and female
effects,
?
̅
?
− ?
̅
𝑓
?
What are the degrees of freedom associated with this estimate?

Practice Final
Stat 311 Spring 2015
9
Problem 6 Regression
Your colleagues have collected some data on the relationship between the time per day that individuals spend cooking
their food (in hours) and the calories per day that people eat. Your goal is to determine if there is a relationship between
the variables. Your colleagues are using time spent cooking as the independent variable.
Fill out the rest of this ANOVA table with numbers (cells to fill out are shaded)
(6.6)
16
21

6.7
How many observations are there in the data set?
6.8
Which test statistic do we use as a general test for model significance in this case?
(circle one)