WARM -UP Through data compiled by the auto industry 12% of Americans are planning on buying a hybrid. A recent national poll randomly asked 500 adults whether they were more likely to buy a Hybrid on their next auto purchase. Find the unbiased Center and Standard Deviation of the Sampling Distribution of . 2. Explain why you can assume normality here. Would it be unlikely to find 16% of Americans planning to buy hybrids? Use the 68-95-99.7% sketch to support your answer. Center = 12% Std. Dev. = 0.01453 np ≥ 10 AND n(1 – p) ≥ 10 500 • .12 = 60 ≥ 10 AND 500 • (1 – .12) = 440 ≥ 10 √

12% of Americans are planning on buying a hybrid. 3. Sketch the Distribution to determine if 16% is unlikely.

SAMPLING DISTRIBUTIONS Chapter 18 SAMPLING DISTRIBUTIONS The Sampling Distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. Center, Shape, and Spread are how we describe a sampling distribution.

SAMPLING DISTRIBUTIONS What proportion of beads are blue?

SAMPLING DISTRIBUTIONS Record a guess to what % of the beads are blue. Each person will come to the front and use the scoop to obtain a random sample of beads. Calculate what proportion of the beads are blue. Record the % on a post-it note and stick on the number line at the appropriate location. (Stack them vertically for duplicate %’s)

The True Proportion of blue beads is 40%. If the True Proportion of blue beads is 40%, what is the probability that you would have scooped a sample of more than 50% blue?...

THE CALCULATIONS of PROBABILITY To calculate the probability of a proportional event: 1. Write down the statement: or Draw the labeled curve, 2. Calculate the z-score, 3. Find the Probability using: normalcdf.

The true proportion of beads that are blue is 40% The true proportion of beads that are blue is 40%. What is the probability that you would have scooped a sample of 30 beads that represented more than 50% blue beads?

Conditions/Assumptions: The true proportion of beads that are blue is 40%. What is the probability that you would have scooped a sample of 30 beads that represented more than 50% blue beads? Conditions/Assumptions: SRS: Random event Approximately normal: 30 • .40 = 12 ≥ 10 AND 30• (1 – .4) = 18 ≥ 10 Independence: 25000 ≥ 10 • 30 = 300

Through polls of polls, 41% of Americans are planning on voting Republican . A recent poll asked 800 adults whether they were more likely to vote for the Republican candidate. 1. Find the probability that over 51% of adults will vote for the republican candidate.

HW PAGE 428: 9,10,13,15,16

Conditions/Assumptions: SRS: Stated Approximately normal: n • p ≥ 10 AND n • (1 – p) ≥ 10 Independence: Population ≥ 10 • n

Through data compiled by the auto industry 12% of Americans are planning on buying a hybrid. A recent national poll asked 500 adults whether they were more likely to buy a Hybrid on their next auto purchase. 1. Find the probability that over 16% of adults will buy hybrids.

II. THE CALCULATIONS of PROBABILITY SAME EXAMPLE: A national political poll asked 2150 adults whether they approved of Congress. Suppose in fact, nationally 28% of all adults said they did. 1. Find the probability that over 30% of adults approve of Congress.

RELATIONSHIPS AND THE DREADED BREAK UP!

SAME EXAMPLE: A national political poll asked 2150 adults whether SAME EXAMPLE: A national political poll asked 2150 adults whether they approved of Congress. Suppose in fact, nationally 28% of all adults said they did. 2. Find the probability that between 25% and 29% of adults approve of Congress.

A statistic used to estimate a parameter is Unbiased if the statistic is equal to or approximately equal to the true value of the parameter for the population.