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AP Statistics

AP Statistics. Section 14.1: Chi-Square Goodness of Fit Test. Objective: To be able to conduct a Chi-Square Goodness of Fit test. Properties of the distribution: All distributions are density curves.

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AP Statistics

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  1. AP Statistics • Section 14.1: Chi-Square Goodness of Fit Test

  2. Objective: To be able to conduct a Chi-Square Goodness of Fit test. Properties of the distribution: • All distributions are density curves. • Each curve begins at 0 on the horizontal axis, increases to a peak and then approaches the horizontal axis asymptotically. • Each curve is skewed to the right. As df increases, the less skewed the curve becomes. • Each curve is identified by its degrees of freedom.

  3. Goodness of Fit Test This test is used to compare a distribution of proportions in a single population with a claimed distribution of proportions (or ratios). • Conditions: • Data is an SRS. • All expected counts are greater than 1. • No more than 20% of the expected counts are less than 5. • Hypotheses: The data follow a specified distribution. The data do NOT follow a specified distribution.

  4. Rejection Region: I will reject if my p-value < . OR I will reject if where df = the number of categories – 1 • Test Statistic & p-value:

  5. State your conclusion in the context of the problem. (2 parts) Ex 1. NCAA records show that in the past ten years 20% of college football players were seniors, 24% juniors, 26% sophomores and 30% freshmen. At PSU there are currently 20 seniors, 29 juniors, 22 sophomores and 18 freshmen. Assuming that the players at PSU can be considered a random sample, does the distribution of players at PSU follow the distribution based on NCAA records?

  6. Ex 2. A rose company distributes seeds in packets of 60. They claim that the ratio of colors of the seeds is 5:4:1 for red to white to pink roses. You randomly select a packet and plant all the seeds. You observe the colors of all the roses and find that you have 28 red roses, 24white and 8 pink. Is there statistical evidence that the seeds to not follow the company’s claim? Test at the level.

  7. Ex 3. The manufacturer of skittles claims that the colors are uniformly distributed. You randomly select a pack and count the colors. You count 14 red, 10 yellow, 5 orange, 18 purple, and 8 green. Is there evidence that their claim is false at the 0.05 level?

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