PSYC 2021
OPTIONAL ASSIGNMENT #2
FEEDBACK
Given are the following situations. What are the hypotheses to study each one.
1.
An educational psychologist wants to show that his/her teaching method yields
better results than the traditional one.
2.
Statistics Canada analyst Brigitte Chavez hypothesizes that while women live
roughly 6 years longer than men, the gap in life expectancy between men and
women is shrinking. i.e. getting smaller.
3.
A parent-teachers’ organization is wondering about the potential health
hazard, i.e. negative effect of wireless technology on children’s behaviour.
4.
Clear-cutting was long considered a safe practice. An environmentalist and most
of society are now concerned about the effect of clear-cutting on the increase
of global warming.
5.
Multiple Sclerosis is largely considered a disease for which there is no cure. An
investigator has proposed a treatment that will decrease the symptoms, and
many patients are waiting for the treatment to become available. The medical
profession doubts the effectiveness of the treatment but agrees to investigate.
6.
It is commonly believed that the average number of boys born in the population
is not influenced by their parents’ socio-economic status. A historian notices that
royal families seem to produce more boys than the general population.
7.
A group of miners has the impression that the amount of gas accumulating in the
mine is higher than environmental standards consider safe. The miners’ union
commissions a study.
8.
It is generally accepted that one hour of physical exercise per day will improve a
person’s health. A health psychologist wants to know whether a substantial
increase will make any difference, either positive or negative.
9.
An economical down-turn has led to an increase of unemployment. Is the degree
to which young people are affected different from that of the general
population?
A.
What are the two contrasting hypotheses?
H0: µ1 = µ0
H0: µ1 ≥ µ0
H1: µ1 ≠ µ0
H1: µ1 < µ0
1
2
3
Note that H0 and H1 cover all possible outcomes.
H0: µ1 ≤ µ0
H0: µ1≥ µ0+X
H1: µ1 >µ0
H1: µ1 < µ0 +X
no difference ; ≠a difference
≥equal or more ; <less
≤ equal or less; more
x
Depending on how behavior
is measured
X less concentration
X more acting out
at least X more; less than X more
x
4
5
6
7
8 x
9 x
x
x
x
x
B.
a.
b.
c.
d.
1
2
3
4
5
6
7
8
9
In each of the situations above, what would a Type I error consist of and who would
bear the cost? What would a Type II error consist of, and who would bear its cost?
Note that these questions can only be answered through careful analysis and not
through superficial guessing.
When considering each of these situations, remind yourself of
what is a Type I error (rejecting a Ho that is actually true)?
what was the Ho in this particular case?
What is the concrete consequence of rejecting the Ho in each of these cases?
Who is affected by the consequence and how?
Go through the same analysis with regards to a Type II error.
TYPE I ERROR
waste resources on ineffective method;
financial cost to school board
Waste of resources searching for factors that
do not exist
Unnecessarily restricting access to wireless
technology, opportunity cost to user
Unnecessarily restricting access to resources
and jobs; economic cost affecting present
Waste of resources on ineffective treatment;
Cost to health system
Introduction of faulty information; possibly
waste of money for useless investigation
Unwarranted attention to an issue that is of
no consequence; waste of resources
Unwarranted attention to a factor that is of
no consequence.
Waste of concern for a population that is no
better or worse off than the rest
TYPE II ERROR
Children miss out on improved method
Missing out on important influences on life
expectancy
Missing out on early detection of health
hazards, long-term cost to user and society
Missing out on opportunity of environmental
protection; long term cost economy & health
Missed opportunity to improve condition;
Cost to patient
Missing out on some nifty piece of knowledge
cost to the intellectually curious
Missing out on a condition that signals hazard
when attention to it could save lives
Missing out on factors that influence health
Overlooking factors that present a problem
to a particular population
C.
Why are scientists preoccupied with alpha (the probability of a Type I error) and not with beta (the
probability of a Type II error?
Two reasons: (1) In scientific investigations a Type I error introduces misleading information which then
becomes very hard to eliminate; Type II errors tend to be eliminated sooner or later provided the error is
reversible. (2) The probability of a Type I error can be known from the z- or t-formula since µ0 is known; the
probability of Type II error can only be known when H 0 is rejected and the probability of a Type II error = 0.
D.
What factors influence the power of a statistical hypothesis test?
(1) the alpha-value chosen, (2) whether test is 1-tailed or 2-tailed, (3) the size of σ or ŝ, (4) z or t, (5) N
E.
What is a point estimate and how does it differ from a confidence interval?
A point estimate is a single value (X ̅); the confidence interval also provides the extent to which µ can
differ from X ̅, on the basis of (1) ŝ, (2) N and (3) α which determines t; α = 1 – C amount of confidence
F.
How is the size of the confidence interval influenced by N?
The size of the confidence interval is influenced by N since the confidence interval = X ̅ ± ŝxbar x t, where
the estimated standard error of the mean ŝxbar = ŝ∕ √N.