ap statistics chp. 11

AP StatisticsChapter 11

Focus Fox1. 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?

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?

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.

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….

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.

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”)

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?


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


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


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


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

Focus Fox

ap statistics chp. 11

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