Practice Questions, Chapter 9
A manufacturer is trying to sell you a batch of 1200 parts. "No more than 2 percent are defective," he insists. He offers to let you take a sample of 100 to test this.
Using a sample of 100 to test for a 2 percent defect rate would violate one of the rules of thumb for using the normal approximation to the binomial distribution. According to the "rules of thumb" for when it is ok to use the normal approximation to the binomial, why is this sample not large enough?
The manufacturer says, "Fine, pick a larger sample then. Look at 200." In terms of the rules of thumb, what is wrong with picking a larger sample?
The hockey team's fans were whining again.
We were the best team during the regular season. Over 80 games, we outscored our opponents by an average of 0.4 goals per game, with a standard deviation of 1.6 goals. Then in a 7-game play-off the other team scored a total of 19 goals and we scored only 17. What is the probability of that?
According to the fans, what is the parameter that describes the population of hockey games? What is the statistic that has them upset? Explain why the statistic might be biased relative to the parameter.
If play-offs were an unbiased sample of hockey games, what would be the probability of the play-off result that took place?
A polling company takes an exit poll of 1000 people in Montana, where 500,000 people vote. They take an exit poll of 2000 people in Florida, where 4 million people vote. Which poll has lower variability? If the true percentage of people voting Democratic in a two-party race was 55 percent, how many people in Florida would the company have to poll in a random sample in order to have a 99 percent chance of finding the percentage of Democratic voters to be between 54.5 and 55.5 percent?
In New York city, 18 percent of men between the ages of 20 and 30 have a pierced ear. Suppose that you take a sample of 500 men in that age group in Muskogee Oklahoma and find that 60 of them have a pierced ear. If Muskogee had the same rate of ear piercing as New York, what would be the probability of your results?