Exercise 17-28: Racquet Spinning
Tennis players often spin a racquet as a random mechanism for deciding who serves first. Is a spun tennis racquet equally likely to land with the label up or down? To investigate this question, a tennis racquet was spun 100 times, with the result that it landed up 46 times.
a. Is .46 a parameter or a statistic? Explain.
b. Clearly identify (in words) the parameter of interest in this situation.
c. Conduct a significance test of whether the sample data provide strong evidence against the hypothesis that the racquet is equally likely to land up or down. Report the hypotheses, test statistic, and p-value, as well as checking the technical conditions.
d. Interpret the p-value. [Hint: This is the probability of what, assuming what?]
e. What test decision would you reach at the α .10 significance level?
f. Explain what is wrong with a conclusion that says: “The sample data provide strong evidence that this tennis racquet would land up 50% of the time in the long run.”
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