Problem
Toss a coin. Coin tossing can illustrate the idea of a sampling distribution. The population is all outcomes (heads or tails) we would get if we tossed a coin forever. The parameter p is the proportion of heads in this population. We suspect that p is close to 0.5. That is, we think the coin will show about one-half heads in the long run. The sample is the outcomes of 20 tosses, and the statistic pˆ is the proportion of heads in these 20 tosses (count of heads divided by 20).
(a) Toss a coin 20 times and record the value of pˆ .
(b) Repeat this sampling process 9 more times. Make a stemplot of the 10 values of pˆ . You are constructing the sampling distribution of pˆ . Is the center of this distribution close to 0.5? (Ten repetitions give only a crude approximation to the sampling distribution. If possible, pool your work with that of other students to obtain several hundred repetitions and make a histogram of the values of pˆ .)
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.