A tennis racquet is spun 100 times, resulting in 46 up and 54
down results. This exercise asks you to assess more formally
whether or not these sample data provide much reason to doubt that
the spinning process would produce 50% for each result in the long
run.
a)Is 0.50 (the proportion form of 50%) a parameter or a
statistic? Explain.
b)Is 0.46 a parameter or a statistic? Explain.
c)Use technology (such as the Reese’s Piecesapplet at the
following website:
http://www.rossmanchance.com/applets/OneProp/OneProp.htm?candy=1)
to simulate 1000 repetitions of this process (spinning a tennis
racquet 100 times), assuming the results are 50/50 in the long run
(Ï€ = 0.5), and calculating the sample proportion of up outcomes for
each of the 1000 repetitions.
d)In how many and what proportion of your 1000 samples was the
proportion of up results either 46% or less or 54% or greater?
e)Use the CLT to approximate the probability of obtaining a
sample proportion of up results of at most 0.46 or of at least
0.54. Is this theoretical approximation close to your simulation
approximation in part d?
f)Does your answer to part e suggest that the observed sample
result (46 up results in 100 spins) is very unlikely to occur by
chance alone if, in fact, the results are 50/50 in the long run?
Explain.
