This assignment covers the standard error, confidence intervals, one-sample tests and two-sample tests (as bonus questions).
statistics
Description
Assignment 3
This assignment covers the
standard error, confidence intervals, one-sample tests and two-sample tests (as
bonus questions). It is out of a total of 60 Marks (plus up to 10 percentage points in
bonus marks for 3 bonus questions). Please show your work and complete
each part in full using the appropriate test.
1. Alcohol
Consumption of Canadian Adults (22
total marks)
We have a random sample of 525
Canadian adults from our own research. We have collected data on their
behaviour surrounding alcohol consumption, specifically the number of drinks
consumed per week on average. We found that the mean for this group is 5.2
drinks per week with a standard deviation of
3.4 drinks.
The Canadian Community Health Survey (from Statistics Canada) had a mean of 4
drinks per week for adult Canadians.
a. What
is the standard error of our statistic? (2 marks)
b. How
would the standard error change if the sample size was only 100? (2 marks)
c. How
would the standard error change if the sample size was 10 000? (2 marks)
d. Draw
the 3 sampling distributions for the 3 samples you’ve just calculated the
standard error for. Draw in the mean, and the number associated with +/-1
standard deviation from the mean,
+/-2 SDs, and +/-3 SDs. (3 marks)
e. What
do b. through d. tell us about sampling distributions, efficiency and sample
size? (2 marks)
f.
Calculate a 95% confidence interval for the
sample of 525 respondents. (3 marks)
g. Now
calculate a 90% confidence interval and a 99% confidence interval for the same
sample. (6 marks)
h. Describe
the size differences in the 3 intervals you’ve just calculated in f. and g.
What does this tell us about the balance between risk that we are wrong, and
level of precision of the intervals we create? (2 marks)
2.
Average commute times across Canadian
cities (20 marks total + bonuses)
In a random sample of Canadian
workers, we found average commute times for respondents working in various
Canadian Cities. For the total population of Canadian workers, the average
commute time was
24.6 minutes with a standard
deviation of 3.1 minutes. At the top for specific cities was Toronto (N=371)
with an average commute time of 52.6 minutes and a standard deviation of 9.8
minutes, followed by Oshawa (N = 152) at 41.6 minutes on average with a standard
deviation of 3.3 minutes. At the other end, we find Thunder Bay (N=76) at 16.7
minutes with a standard deviation of 1.6 minutes followed by Moncton (N=32) at
17.7 minutes with a standard deviation of 2.0 minutes. Use an alpha of .01 for
tests in this section.
a.
Are any of these specific cities significantly
different from Canadian average commute times?
Note you should have 1 test for each city here. (20 marks)
b. Is
Toronto significantly higher than Oshawa in terms of average commute times? (bonus)
c. Is
Thunder Bay significantly lower than Moncton in terms of average commute times? (bonus)
3. Sense
of Community in London (18
total marks + bonus)
We are looking at 2 different
neighborhoods in London Ontario and we are interested in sense of community
belonging. One of the questions asked on a survey given out to respondents in
each neighborhood asked whether they know at least one neighbor they could
count on in an emergency. In Neighborhood 1 (N=139), 35% knew at least one
neighbor in this way. In Neighborhood 2 (N=106), 39% did. For London as a
whole, we know that 37% of respondents answered yes to this question as part of
a recent National Survey.
a. Create
99% confidence intervals for each of the two neighborhoods (6 marks)
b. Do
the intervals overlap? What does something like that tell us about differences
between these neighborhoods? (2 marks)
c. Is
Neighborhood 1 significantly less likely to say yes to this question than
Londoners overall? (5 marks)
d. Is
Neighborhood 2 significantly more likely to do so? (5 marks)
e. Are
the two neighborhoods significantly different from each other in the likelihood
that they know at least one neighbor they can count on in an emergency? (bonus)
