Recall from Exercise P.2.5 the data on duration of NFL football games in 2012 for the first three weeks of the season, when replacement referees officiated the games, and for the next three weeks when the regular referees returned to officiate the games. Dotplots of these data are reproduced in the following dotplots. The data appear in the file Referees.
a. Identify the observational units and variables in this graph. Also identify which variable is explanatory and which is response and classify the variables as categorical or quantitative.
b. Did the data collection for this study make use of random sampling, random assignment, or neither? Explain.
c. Before you conduct an inferential analysis, what do the dotplots suggest with regard to the question of whether game durations differed for the two types of referees?
d. State the appropriate hypotheses for testing whether the long-run average game duration is different for games played with replacement referees as compared to games played with regular referees.

e. Use an applet to simulate a randomization test for testing the hypotheses in part (d) and find the p-value.

f. Interpret what this p-value means in this context.

g. Use the simulation results to produce a 95% confidence interval for the relevant parameter.

h. Interpret this confidence interval.
i. Summarize your conclusions from these data. Make sure you address significance, confidence, generalization, and causation.

Transcribed Image Text:

Regular Replacement 200 210 Duration (mins) 190 170 180 220 230 240 Replacement Refs?