Successfully reported this slideshow.
Upcoming SlideShare
×

# Ap statistics chp. 11

558 views

Published on

expected vs observed counts

• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

### Ap statistics chp. 11

1. 1. AP Statistics Chapter 11
2. 2. Focus Fox 1. Using six words, describe your spring break: 2. How will you select the individuals in your sample for your significance test? 3. In general, what is the claim you wish to test?
3. 3. Inference -Dist. by Categories By the end of this chapter, we will be able to answer questions like the following: - Are births evenly distributed across the days of the week? - Does background music influence customer purchases? - Is there an association between anger level and heart disease? - Is the distribution of the colors of skittles in each package true to expected distribution produced in the factory?
4. 4. What’s in Your Package?? Assuming the company’s claim is true, we would expect 24% of the M&M’s to be blue. If you had 60 M&M’s in your package, how many should be blue?? Compute the expected counts for your bag and record your results in the “Expected” column of your table. Check that the sum of the expected counts equal the number of M&M’s in your package.
5. 5. What’s in Your Package?? How close are your observed counts to the expected counts? Calculate the difference for each color and record in your table: Observed – Expected *What do you notice about the ∑ (Observed – Expected)?? Since the difference = 0, this does not help us determine how far off your package is from the claim….
6. 6. What’s in Your Package?? So square all the values (remember variance and stnd dev) Compute the squared values for the differences in the observed and expected counts and find the sum. Compare your results with your peers.
7. 7. What’s in Your Package?? The last column has you divide the difference by the expected count for each color – this is a distance difference The sum of this column is called a chi-square statistic denoted by χ2. (similar to our “z-score”)
8. 8. What’s in Your Package?? If your sample reflects the claim - Your observed should be close to your expected - Your values making up χ2 should be very small Are the entries in the last row all similar or does one stand out as much larger or much smaller than the others? Did you get way more or way less than expected of one color? Compare your χ2 with your peers’ χ2 answers. Does anyone have a χ2 that provides convincing evidence against the company’s claim?
9. 9. Inference -Dist. by Categories We could run a 1 sample test on each color, but… - That is inefficient and we would get conflicting results - That wouldn’t tell us how likely it is to get a random sample of 60 candies with a color distribution that differs as much from the one claimed by the company of all colors at one time Need a new test: chi-square goodness-of-fit test
10. 10. Inference -Dist. by Categories Null hypothesis in chi-square goodness-of-fit test: - States the claim about the distribution of a single categorical variable in the population of interest H0: The company’s stated color distribution for M&M’s Milk Chocolate Candies is correct Alternative hypothesis in a chi-square goodness-of-fit test: - States the categorical variable does not have the specified distribution Ha: The company’s stated color distribution for M&M’s Milk Chocolate Candies is not correct
11. 11. Inference -Dist. by Categories H0: The company’s stated color distribution for M&M’s Milk Chocolate Candies is correct Ha: The company’s stated color distribution for M&M’s Milk Chocolate Candies is not correct Hypotheses can also be written as: H0: pblue = 0.24, porange = 0.20, pgreen = 0.16, pyellow = 0.14, pred = .13, pbrown = .13 Ha: at least one of the pi’s is incorrect
12. 12. Inference -Dist. by Categories Caution: DON’T state the alternative in a way that suggests the all the proportions in the hypothesized distribution are wrong H0: pblue ≠ 0.24, porange ≠ 0.20, pgreen ≠ 0.16, pyellow ≠ 0.14, pred ≠ .13, pbrown ≠ .13 Goal: to compare observed counts with expected counts IF null is true The more the observed counts differ, the more evidence we have against the null
13. 13. Focus Fox