WARM UP A statewide poll reveals the only 18% of Texas household participate in giving out Halloween Treats. To examine this you collect a Random Sample of 120 Texas households. 1. What is the Probability that less than 12% of Texas households give out Treats? 2. Comment on the validity of your results by checking the Rule of Thumb assumptions. RULE OF THUMB #2: ≥ 10 AND 120 (1 –.18) ≥ 10 RULE OF THUMB #1: Pop. of Texas Households ≥ Draw the Sampling Distribution curve.

N(0.18, 0.035)

Sample Proportion, use Categorical Data Data collected by COUNTING. Sample Means, use Quantitative Data Data collected by AVERAGING Chapter 18 (continued)

SAMPLE MEANS (Chapter 18 continued) The unknown Population Mean is a parameter with the symbol of:. The Population Standard Deviation has the symbol: The Sample Mean is a statistic with the symbol of: and the Sample Standard Deviation has the formula. I. THE BASICS

ASSUMPTIONS for Sample Means: #1: The sample was collected using an SRS. #2: Approximate Normal: 1. Large n = (n ≥ 30), OR 2. Stated that its Normal, OR 3. You construct an approximately Normal Histogram/Boxplot from the given data.

It is known that each individual Halloween Treat given out has about 120 calories with standard deviation of 50. To examine this you collect a Random Sample of 40 Halloween treats. 1. What is the Probability that the sample average is less than 100 calories? 2. Comment on the validity of your results by checking the conditons/assumptions. Approximately Normal due to the Large n. Stated to be a Random sample 3. Draw the Sampling Distribution curve.

II. THE CALCULATIONS 1.Find the Mean and Standard Deviation of the Sampling Distribution of. 2.Explain why you can assume normality in the sample. Mean = 3.5 Std. Dev. =.1697 #1: The sample was collected by an SRS #2: Approximately Normal b/c Large n EXAMPLE: A national political poll asked a SRS of 50 adults to give an approval rating of President Obama’s Job in office using a scale from 1 (Low) to 10 (High). Suppose in fact, nationally Obama’s rating has a Mean of 3.5 and Standard Deviation of 1.2

3.Find the probability Obama has a rating over 4.0. II. THE CALCULATIONS of PROBABILITY SAME EXAMPLE: A national political poll asked a SRS of 50 adults to give an approval rating of President Obama’s Job in office using a scale from 1(Low) to 10(High). Suppose in fact, nationally Obama’s rating has a Mean of 3.5 and Standard Deviation of 1.2

4. Find the probability Obama’s approval rating is between 3.2 and 4.0. SAME EXAMPLE: A national political poll asked a SRS of 50 adults to give an approval rating of President Obama’s Job in office using a scale from 1(Low) to 10(High). Suppose in fact, nationally Obama’s rating has a Mean of 3.5 and Standard Deviation of 1.2

Finding Sample Mean Observations, (x) from Probabilities EXAMPLE: Assume that the duration of human pregnancies is Appr. Normal with mean: 266 days and Std Dev.: 16. At least how many days should the longest 25% of all pregnancies last? x=? z = invNorm(.75)=.6745 x = %

Finding Sample Mean Observations, (x) from Probabilities EXAMPLE: Assume that the rainfall in Ithaca, NY is Appr. Normal with mean: 35.4 inches and Std Dev.: 4.2”. Less than how much rain falls in the driest 20% of all years x=? z = invNorm(.20)= x = ” 20%

1. The Test over Chapter ninteen has traditionally had a mean of 86.2% with a std. deviation of 8.5%. Assume the data follows a Normal distribution. a.) If a student is selected at random, what is the probability that he or she will score above 90%? b.) If 16 students are selected at random, what is the probability that their average will be above 90%? c.) Draw the Sampling Distribution Normal Curves for both a and b. On both graphs label all six standard deviations (± 3s) for the.

With μ = 86.2% and σ = 8.5%. a.) When n = 1 the b.) When n = 16 the c.)