In a study conducted in New Zealand, Parkin et al. randomly assigned volunteers to either wear socks over their shoes (intervention) or wear usual footwear (control) as they walked downhill on an inclined icy path. Researchers standing at the bottom of the inclined path measured the time (in seconds) taken by each participant to walk down the path. Here are the summary statistics. Note that the data are fairly symmetric in both groups.

The research question to be addressed through the following questions is: Do the data provide evidence that people wearing socks over their shoes will take a shorter time to walk down an icy, steeply inclined road, on average, compared to those wearing usual footwear?
a. Describe the parameter(s) of interest in the context of this study.
b. State the null and the alternative hypotheses in the context of the study.
c. Name the appropriate theory-based method you would use to test the hypotheses stated in part (b).
d. State the validity conditions that have to be met to be able to perform the test named in part (c). Are these conditions met? How are you deciding?

e. Regardless of your answer to part (d), perform the theory-based test proposed in part (c). Be sure to report a test statistic value and a p-value.
f. Determine a 95% confidence interval for comparing the walking time between the two groups.

g. Summarize your conclusions about the research question of the study. Be sure to comment on statistical significance, confidence/estimation, causation, and generalization.

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Mean SD Intervention 9.36 14 37.7 Control 39.6 15 11.57