# Sample Proportion and The Population Proportion Discussion

-For which of these coin-tossing scenarios are you most likely to get heads on every toss? Explain your answer.

Toss a coin 3 times.

Toss a coin 5 times.

Toss a coin 10 times.

-Name three different ways you can find probabilities for the Normal distribution.

-Discuss why probabilities for the normal distribution and other continuous distributions are the same as areas under the curve for a given interval.

-Discuss the differences between the sample proportion and the population proportion. Which is random and which isn’t? Why?

-What does it mean to be “95% confident” in your estimate? Why can’t you be 100% confident?

-When you’re using sample data to describe a population, why is it important to use a random sample?

-What is the significance level of a hypothesis test? Is the significance level a necessary part of the test?

-What is the trade-off for increasing the level of confidence in an estimate?

-When estimating a population proportion using the sample proportion, what is margin of error and why is it necessary?

-Is it possible to be 100% confident when using a confidence interval to estimate a population characteristic? Explain

-The chance of winning the Mega Millions lottery jackpot is 1 in 303 million. If the chance is that low, how come there are winners?

-When estimating a population characteristic based on a sample statistic, why it is important to use standard error as part of your estimate?

-Discuss the law of averages and how it can be used to analyze a gambler’s long run success or failure. Does the law of averages mean there’s no such thing as luck?

-Discuss how the standard normal distribution, Z, lets you compare apples to oranges.