Warm Up A normal distribution has a mean of and a standard deviation of 9.3. use the standard normal table on page 248 to find the indicated probability for a randomly selected x-value from the distribution. 1.) P(x ≤ 104.3)2.) P(x ≥ 90.9)3.) P(123.1 ≤x≤142.3)

6.3 – APPROXIMATE BINOMIAL DISTRIBUTIONS AND TEST HYPOTHESES Unit 6 – Data Analysis and Probability

Georgia Performance Standards MM3D2b – Determine the probability that a given value falls within a specified interval MM3D2c – Estimate how many items in a population fall within a specified interval. MM3D3 – Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

Vocabulary To test a hypothesis about a statistical measure for a population, use the following steps:  Step 1 – State the hypothesis you are testing. The hypothesis should make a statement about some statistical measure of a population.  Step 2 – Collect data from a random sample of the population and compute the statistical measure of the sample.  Step 3 – Assume the hypothesis is true and calculate the resulting probability P of obtaining the sample statistical measure or a more extreme sample statistical measure.

Hypothesis Example

MEAN: x= np STANDARD DEVIATION σ=√np(1-p)

Example 1: Find a binomial probability According to a survey conducted by the Harris Poll, 23% of adults in the United States favor abolishing the penny and making the nickel the lowest denomination coin. You are conducting a random survey of 500 adults. What is the probability that you will find at most 106 adults who favor abolishing the penny?

Example 1: Things to Consider 1. What are you trying to find? (Key words) 2. What does the problem give you and what can you find? 3. Are their any formulas that can help? 4. Is there a distribution I can use?

Example 1: Work Find the mean ( x = np) Find the standard deviation (σ=√np(1-p) Sketch the normal distribution curve  Label the mean  Label your standard deviations

Example 2: Test A Hypothesis A recent Harris Poll claimed that 44% of adults cut back on their spending in order to pay the increased price of gasoline. To test this finding, you survey 60 adults and find that 21 of them cut back on their spending in order to pay the increased price of gasoline. Should you reject the Harris Poll’s findings? Explain.

Example 2: Test A Hypothesis Step 1: State the Hypothesis  44% of adults cut back on their spending in order to pay the increased price of gasoline. Step 2: Collect data  In your survey, 21 out of 60, or 35%, cut back on their spending in order to pay the increased price of gasoline. Step 3: Assume  Find the resulting probability that you could randomly select 21 or fewer adults out of 60 who have cut back on their spending to pay the increased price of gasoline.

Example 2: Test A Hypothesis Find the mean Find the standard deviation Find the z-score!

Guided Practice 1 & 2 Try Guided Practice for examples 1 & 2

Classwork/Homework Page 226: 1-17