WARM – UP 1. Phrase a survey or experimental question in such a way that you would obtain a Proportional Response. 2. Phrase a survey or experimental question in such a way that you would obtain a Mean Number Response. 3. What is the difference between a Parameter and a Statistic?` What Proportion of Coin Tosses result in “Heads”? What is the Average year of a bag of 300 Pennies? Parameter = Population, Statistics = Calc. from Sample.

RELATIONSHIPS AND THE DREADED BREAK UP!

SAMPLING DISTRIBUTION Chapter 18 SAMPLING DISTRIBUTION 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.

SAMPLE PROPORTION I. THE BASICS The unknown Population Proportion is a parameter with the symbol of: The Sample Proportion is a statistic with the symbol of: 1. If collected properly (SRS) the sampling distribution of a sample proportion, , has an approximately normal shape when ‘n’ is large.*** 2. The mean is approximately equal to the population .

3. The standard deviation of a sampling distribution for 3. The standard deviation of a sampling distribution for sample proportions is calculated by: 4. The formula for the Standard Deviation of p-hat is only accurate and reliable when the population is at least 10 times as large as the sample: INDEPENDENCE RULE: Pop. ≥ 10 • n 5. ***The assumption that the sample distribution of p-hat is approximately normal is valid if and only if: APPR. NORM. RULE: n • p ≥ 10 AND n • (1 – p) ≥ 10

Modeling the Distribution of Sample Proportions (

EXAMPLE: One of the students in the introductory statistics class claims to have tossed her coin 200 times and found only 84 heads. What do you think about this claim? Is it unusual? 95% .394 .429 .465 .5 .535 .571 .606 CHECK THE ASSUMPTIONS!!!!!!!!!!!!!!!! Pop. ≥ 10 • n Pop. ≥ 10(200)√ np≥10 AND n(1 – p) ≥10 200 • .5 = 100 ≥ 10 AND 200 • (1 – .5) = 100 ≥ 10 √

2. Explain why you can use the Std. Dev formula. II. THE CALCULATIONS EXAMPLE: A national political poll randomly asked 2150 adults whether they approved of the President’s Job in office. Suppose in fact, nationally 72% of all adults said they did. 1. Find the Mean and Standard Deviation of the Sampling Distribution of . 2. Explain why you can use the Std. Dev formula. 3. Explain why you can assume normality here. Mean = 72% Std. Dev. = 0.0097 INDEPEDENCE : Pop. ≥ 10 • 2150 = 21500 √ APPR. NORM. RULE: 2150•.72=1548 ≥ 10 AND 2150(1 – .72)=602 ≥ 10 √

Page 428:1,3,7,8, 11,12 .077 .139 .202 .264 .326 .389 .451 CHECK THE ASSUMPTIONS!!!!!!!!!!!!!!!! Pop. ≥ 10 • n Pop. ≥ 10(50) = 500√ np≥10 AND n(1 – p) ≥10 50 • .264 = 13.2 ≥ 10 AND 50(1 – .264) = 36.8 ≥ 10 √

a.) The shape is expected to be symmetric, but the sample size is too small to guarantee that. b.) The histogram is expected to have its center at 0.5 c.) The variability is the standard deviation of data: d.) The expected number of heads, np = 16(0.5) = 8, which is less than 10. The Success/Failure condition is not met. The Normal model is not appropriate in this case.

Virtual Dice Experiment Seed your calculator with any random number. Model the probability of rolling a die by typing the following: STAT EDIT L1 MATH  Prb  #5 RandInt(1,6,60) Simulate the rolling of 60 die and count the number of times out of 60 that you obtain a each outcome. “1-6”(Press Enter 60 times). Count the number of 5’s 60

SAMPLING DISTRIBUTION Chapter 18 SAMPLING DISTRIBUTION 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.