2390 Lab 6 in progress
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KWANTLEN
POLYTECHNIC UNIVERSITY
Geog 2390
F Semester 2023
John E. Martin
Quantitative Methods
Lab Assignment: Hypothesis testing - One, Two and Paired
A: Formulating Hypotheses
1. Write out the following ideas as mathematical sentences using =, ≠, >, ≥, etc. State the (i) null
and (ii) alternative hypotheses (e.g. H
0
= µ ≤ 0; H
A
= µ > 0). See text and note for more. (2)
(a)
A manufacturer claims the mean lifetime of its AAA size batteries
is more than 16
hours
.
Null Hypothesis = H
0
= µ ≤ 16 hours
Alternative Hypothesis = H
A
= µ > 16 hours
(b)
A student says the mean cost of a used statistics textbook
is less than $125
.
Null Hypothesis = H
0
= µ ≥ $125
Alternative Hypothesis = H
A
= µ < $125
2. The claim is that
greater than 88%
of students at KPU have a smart phone. Would you apply
a
right-tailed, left-tailed, or two-tailed test
?
Draw the diagram
of the distribution and briefly
explain which is is, and why. (3)
The value indicates greater than 88% of students. So, I would prefer to use the right tailed test.
Null Hypothesis: H
0
= µ ≤ 88% or 0.88
Alternative Hypothesis: H
A
= µ > 88% or 0.88
The critical area here is rejecting the null hypothesis.
3. For this question,
a paired t test
(samples collected in “pairs”) has been run in Excel and you
will interpret the output. Zinc concentrations were measured in water storage tanks in the interior
of BC (see
Zinc tab
). Measurements were made in
10 randomly selected tanks
at the surface
and bottom of the tanks. The question asked by authorities, “Is the bottom water
higher in zinc
concertation
than the surface water at the
95% confidence level
?”
The
paired t test
has already been run for you (95% confidence), with the result output
presented in the Excel file. Regions in the table have been
bolded to provide some clues (or
misclues!).
(a)
State the null and alternative hypothesis for the
paired t test for means
.
Null Hypothesis:
(b) Diagram the regions of rejection/non-rejection, noting if this a one or two tailed test.
(c) Decide regarding the
null and alternative hypothesis
. Completely explain your
decisions referencing the data provided. Paste/record the results in a word file.
2
(d) In this specific case, what would be a
Type I error
, and what would be a
Type II
error
? (8)
B: One-Sample t test
1. According to a 2005 US Government study, the annual average water usage per household
(small resort type) in the
US is 37,500 gallons
(note SD not known or stated). A local
environmental group believes that household water consumption in a small town is
too high,
and
it wants the municipal government to take steps to reduce water consumption.
Before agreeing to such a campaign the municipal government wants to be
90% confident
that
local water consumption is
higher
than the national average. You have 40 randomly sampled
local households, and the results are in the
Water Use tab
of
Lab 6
.
Follow the steps of formal hypothesis testing (below) to evaluate whether the local water
consumption
is higher than
the US national average. Provide a one or two sentence explanation
or rationale for each step as appropriate. Manually write out all the values and formulas but
use
Excel to do the actual calculations
in the designated areas of the spread sheet and copy the
results to your word file lab.
I.
Clearly state Null and Alternative hypothesis (watch your format)
II.
Select appropriate statistical test (
t
or
z
, one or two tails)
III.
Identify level of significance
α
or
α/2
IV.
Diagram the regions of rejection and non-rejection of the null hypothesis (one or two
tails)
V.
Calculate the
test statistic
(for this it will be “by hand” in Excel)
VI.
Make decision regarding the
null
and
alternative hypothesis
. Provide two pieces of
evidence to support your answer and briefly explain why. (12)
C: Two-Sample t test
The tab
life expectancy
lists 30 countries (randomly chosen) from two larger groups of
developed countries
(Dev 2009) and
less developed countries
(LDev 2009) from statistics
collected in 2009. The UN would like to know if the
means are equal
from the groups.
1. Note that you will first have to determine if the
variances are equal
, or close to equal, by
running an
F test
on the data sets (at 95% confidence). (a) State the null and alternative
hypothesis for the
F test on the variances
.
(b) Run the F test using the data tool pack functions.
Note variable #1 must have the
greater variance
(as a quirk of Excel, this is to ensure that the value of the F statistic is
greater than 1). If it does not,
rerun the test by switching variable 1 and variable 2
in
the input options. Again, use the F test where variable 1 has the greater variance.
c) Decide regarding the
null and alternative hypothesis
for the variances and explain
you’re your results mean. Paste the table of results in a word file. (6)
2. Once you have determined if the variances are equal or not, choose the
appropriate t test
(at
95% confidence) from the data analysis tool as shown in the window below.
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