Elementary Statistics Lab Assignment 8

An important example of a binomial random variable comes from opinion polls. For example,suppose you take an SRS of 1000 registered voters and ask each one, “Do you approve of the jobPresident Bush is doing?” If the true fraction of the population who think President Bush is doinga good job is 0.47, then this is a binomial experiment with 1000 trials (the 1000 voters sampled)and probability of success 0.47 (the probability that a voter will think President Bush is doing agood job).Let’s look at a binomial experiment in which the probability of a success is relatively small, sothat we can see what happens when we sample from a skewed distribution. First generate 1000tosses of an unfair coin with probability of heads equal to 0.1. To do this, use the random numbergenerator in the analysis tools. Type in 1 variable and 1000 numbers. Pull down the menu fordistribution and select “binomial.” For p-value, enter 0.1, and for number of trials enter 1. Thiswill give 1000 values, about 10 percent 1 and about 90 percent 0. Make a histogram with two barsshowing the distribution of these values. What’s the mean? What’s the standard deviation?Now let’s “sample” the population, by generating 1000 samples of size 10. On another worksheet,go back to the random number generator. This time select 10 variables, 1000 numbers, anda binomial distribution with p-value 0.1 and 1 trial. (In case you’re wondering, our trials are the10 individual samples.)Find the mean of the number of 1’s in each sample, and make a histogram of these means. Doesthis distribution look normal?If you have any extra time, try repeating this problem with samples of size 100 instead ofsamples of size 10. How does this affect the distribution of the sample means?What to Turn InYou should turn in the following material.1. A copy of your histogram showing the distribution of the sample means from a normal distribution(similar to figure 10.3).2. A copy of your histogram showing the uniform distribution.3. A copy of your histogram showing the distribution of the means of the samples taken fromthe uniform distribution.4. A copy of your histogram showing the distribution of the number of successes in a binomialexperiment with p-value 0.1.5. A copy of your histogram showing the distribution of the means of the samples taken fromthe binomial distribution.2