STAT 252 LAB 1 University of Alberta STAT 252 (Questions and Answers)
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Course
STAT 252
Institution
STAT 252
1. Comment on the study design. In particular, is this an observational study or
experimental study? What kind of inference or interpretation can you make? Is it
possible to establish a causal link between the speed limit increases and the
change in interstate traffic fatalities using this data?...
1. Comment on the study design. In particular, is this an observational study or
experimental study? What kind of inference or interpretation can you make? Is it
possible to establish a causal link between the speed limit increases and the
change in interstate traffic fatalities using this data? What is the population of
interest? Can the findings be generalized to this population?
This is an observational study as the data has been collected from previous study and
the researcher has had no control over the variables. It is not possible to establish
causal links within observational studies as the experiment cannot be manipulated to
test different variables. The researcher can only make inferences on what is naturally
observed, so a cause and effect relationship cannot be determined. The population of
interest is all 50 U.S. states and the District of Columbia. Since the study is simply
observational and not controlled, the findings cannot be generalized. There are many
factors that could have contributed to the number of interstate traffic fatalities such as
road conditions, state of driver (intoxicated, tired, etc.), or condition of the vehicles
driven.
2. Use the Explore procedure to obtain the descriptive statistics, the side-by-side
boxplots, and the normality plots of percentage change in interstate traffic
fatalities from 1995 to 1996 for states that increased speed limits and for those
that didn’t.
(a) Obtain and paste the descriptive statistics for the percentage change in
interstate traffic fatalities for both sets of states into your report. Compare the
means and standard deviations of the two distributions.
The mean of percent change for states that did not increase their speed limit is -8.5632
with a standard deviation of 31.00085. The mean of percent change for states that did
increase their speed limit is 13.7531 with a standard deviation of 21.33285.
Descriptives
increase Statistic Std. Error
, Lily Schmitke
ID# 1579364
percentchg .00 Mean -8.5632 7.11208
95% Confidence Interval for Mean Lower Bound -23.5051
Upper Bound 6.3788
5% Trimmed Mean -7.5202
Median -9.7000
Variance 961.052
Std. Deviation 31.00085
Minimum -80.00
Maximum 44.10
Range 124.10
Interquartile Range 35.80
Skewness -.222 .524
Kurtosis .480 1.014
1.00 Mean 13.7531 3.77115
95% Confidence Interval for Mean Lower Bound 6.0618
Upper Bound 21.4444
5% Trimmed Mean 13.5465
Median 12.1000
Variance 455.090
Std. Deviation 21.33285
Minimum -31.50
Maximum 62.50
Range 94.00
Interquartile Range 31.18
Skewness .123 .414
Kurtosis -.133 .809
(b) What is the 95% confidence interval for the mean percentage change in traffic
fatalities from 1995 to 1996 for each group (confidence interval can be obtained
from the descriptive statistics in part (a)). Which interval is wider? Explain why the
wider one is wider. Are the two confidence intervals overlapping? What does this
mean?
The confidence interval for the group with no speed increase is (-23.5051, 6.3788) and
the confidence interval for the group with a speed increase is (6.0618, 21.4444). Both
means are contained in the confidence intervals. The interval for the group with no
speed increase is wider. This is because it has a larger standard error, and a smaller
sample size. The intervals are overlapping meaning the difference between the two
groups is not statistically significant.
(c) Based on your intervals in part (b), does it appear that traffic fatalities
increased for those states that increased their speed limits? What about for those
that retained the speed limits?
The interval for states that did not increase their speed limits contains zero. This means
that there was no change in the number of fatalities. The interval for states that did
increase their speed limits is well above zero meaning the number of fatalities increased.
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