Sampling Distribution WELCOME to INFERENTIAL STATISTICS

Frequency Distribution Normal (Gaussian) Distribution Probability Distribution Poisson Distribution Binomial Distribution Sampling Distribution t distribution F distribution Types of Distribution

AP EXPECTATIONS COMPLETE WORK ON TIME, EVERY TIME KEEP YOUR NOTES ORGANIZED SHOW MATURITY BE RESPONSIBLE Am I an AP Statistics student material?

QUESTION 1 On a 10-item multiple-choice quiz with 4 choices, what is the probability that you will get 7 of the problems correctly by guessing

QUESTION 2 According to ACCU Weather, the chance of raining in Barstow from Monday-Friday is 43%. What is the probability that it will rain from Monday till Wednesday?

QUESTION 3 Shelby is a high school basketball player(yeah right). She is a 70% free throw shooter. During this season, what is the probability that Shelby miss her free throw on her 4th free throw shot?

QUESTION 4 With a 70% accuracy, how many shots do you think Shelby is expected to contribute to his team given that she gets to do 24 free throw shot in this game?

QUESTION 5 Austin needs to get a 1 on his 5th roll to beat Krista on the game of Monopoly. What is the probability that Austin keeps his title on the game of monopoly?

QUESTION 6 What is the expected number of rolls before a 1 come out in this monopoly match?

QUESTION 7 What is the difference between geometric distribution and binomial distribution?

answers 1. P(x=7).0030 or.30% 2. P(x≤3).8878 or 88.78% 3. P(x=4).0189 or 1.89% 4. µ=np (.70)(20) = 14 shots 5. P(x=5).0804 or 8.04% 6. µ= 5 rolls 7. Binomial distribution has definite number of trials

A sampling distribution is created by, as the name suggests, sampling. The method we will employ on the rules of probability and the laws of expected value and variance to derive the sampling distribution. For example, consider the roll of one and two dice… What is Sampling Distribution?

x P(x) 1/6 A fair die is thrown infinitely many times, with the random variable X = # of spots on any throw. The probability distribution of X is: …and the mean and variance are calculated as well:

Sampling Distribution of Two Dice A sampling distribution is created by looking at all samples of size n=2 (i.e. two dice) and their means… While there are 36 possible samples of size 2, there are only 11 values for, and some (e.g. =3.5) occur more frequently than others (e.g. =1).

Sampling Distribution of Two Dice… The sampling distribution of is shown below: P( ) 6/36 5/36 4/36 3/36 2/36 1/36 P( )

…with the sampling distribution of. Compare the distribution of X…

1) The statistic of interest (Proportion, SD, or Mean) 2) Random selection of sample 3) Size of the random sample (very important) 4) The characteristics of the population being sampled. The 4 features of sampling distribution include:

Statistic vs. parameter A statistic is a quantity that is calculated from a sample of data A parameter is a value, usually unknown (and which therefore has to be estimated), used to represent a certain population characteristic  p x, s, p In real life parameters of populations are unknown and unknowable. –For example, the mean height of US adult (18+) men is unknown and unknowable

PARAMETER VS. STATISTIC In real life parameters of populations are unknown and unknowable. – For example, the mean height of US adult (18+) men is unknown and unknowable Rather than investigating the whole population, we take a sample, calculate a statistic related to the parameter of interest, and make an inference. The sampling distribution of the statistic is the tool that tells us how close the value of the statistic is to the unknown value of the parameter.