STAT 252 LAB 1 University of Alberta STAT 252 (Questions and Answers)

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# 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. Lily Schmitke ID# (d) Using the “select cases” function in the data menu, carry out individual one-sample t-tests to determine if percentage change in fatalities is different from 0 for each group of states. Paste the output into your report. Simply refer to the p-value in the SPSS output and answer the question. Do these agree with those in part (c)? One-Sample Statistics N Mean Std. Deviation Std. Error Mean percentchg 19 -8.5632 31.00085 7.11208 One-Sample Test Test Value = 0 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper percentchg -1.204 18 .244 -8.56316 -23.5051 6.3788 The p-value for the group with no speed increase is 0.244 which is significantly different from zero. This result agrees with the conclusion in part (c) that states there was no change in fatalities. One-Sample Statistics N Mean Std. Deviation Std. Error Mean percentchg 32 13.7531 21.33285 3.77115 One-Sample Test Test Value = 0 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper percentchg 3.647 31 .001 13.75312 6.0618 21.4444 The p-value for the group with a speed increase is 0.001, this result agrees with the conclusion in part (c) that states there was an increase in fatalities among states who increased their speed limits. (e) Obtain and paste the side-by-side boxplots of percentage change in traffic fatalities for the two groups into your report. Compare the centers and spreads of the two distributions. Compare your results to those in part (a). Comment about the shape Lily Schmitke ID# (symmetric, skewed, or neither) of each distribution. Are there any outliers? Comment on the assumption of equal variability for the two independent sample t-tools. Is there any evidence that this assumption may be seriously violate In both plots the data is reasonably close to the line meaning the normality assumption is satisfied. The center of the distribution for the group with no increase is significantly lower than the increased group. The spread of the group with a speed increase is much higher than the group with no increase, with the max percent change being well over 50. These results are the same as in (a), with the mean of the non increased group being under zero. The distribution for the group with no increase is slightly right skewed. The third observation is the only outlier. The distribution for the group with an increase in speed limit is right skewed with no outliers. (f) Obtain and paste the normality plots for each distribution into your report. Comment on the assumption of normality for the t-tools. Is there any evidence that this assumption may be seriously violated? 3.) Now you will use the appropriate t-tools to analyze the data. Consider the difference in average percentage change in traffic fatalities for the states that increased the speed limit versus those that retained the speed lim