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Project

Explore various statistical analysis case studies including M&M candies, coffee consumption survey, dogs ownership data, birth distribution, age demographics, lotto ticket buyers, and genetic traits inheritance. Understand chi-square tests and their applications.

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Project

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  1. Project • Make sure both parts are turned in today • We are not working on them during class time

  2. Is my sample of M & M’s unusual?

  3. Fill out this table for YOUR sample of M & M’s

  4. M&M Suppose that we have a simple random sample of 600 M&M candies with the following distribution: • 212 of the candies are blue. • 147 of the candies are orange. • 103 of the candies are green. • 50 of the candies are red. • 46 of the candies are yellow. • 42 of the candies are brown.

  5. M&Ms • Find the expected counts for each color • Find the chi-square value • Find the degrees of freedom • Find the p-value • Is this bag unusual?

  6. Coffee Researchers have conducted a survey of 1600 coffee drinkers asking how much coffee they drink in order to confirm previous studies. The results of previous studies (left) and the survey (right) are below. At α = 0.05, is there enough evidence to conclude that the distributions are the same?

  7. Pronunciation guide: • You could say chi (like sky) • (that’s how I’ve always heard it!) • You could say chi (like key) • (which is apparently how the Greeks say it) Introduction to the 𝜒2 test (Read as a chi-squared test)

  8. Ready? • Randomly selected sample • 10n < N • All expected counts at least 5 Conditions for a 𝜒2 test

  9. Χ2 ≥ 0 • Asymptotic to horizontal axis • Family of curves denoted by……df! The Χ2 Distribution

  10. Dice • Is your die fair? • You will roll your die 50 times. Record your results

  11. Gather Data • Design a question to ask the class that has 3 answer choice options • Does your data show evidence that your answer choices were equally likely?

  12. Dogs The American Pet Products Association conducted a survey in 2011 and determined that 60% of dog owners have only one dog, 28% have two dogs, and 12% have three or more. Supposing that you have decided to conduct your own survey and have collected the data below, determine whether your data supports the results of the APPA study. Use a significance level of 0.05. Data: Out of 129 dog owners, 73 had one dog, 38 had two dogs, and 18 had three or more.

  13. Acme Toy Company prints baseball cards. The company claims that 30% of the cards are rookies, 60% veterans, and 10% are All-Stars. Suppose a random sample of 100 cards has 50 rookies, 45 veterans, and 5 All-Stars. Is this consistent with Acme's claim? Use a 0.05 level of significance.

  14. Are births evenly distributed across the • days of the week? The one-way table below • shows the distribution of births across the days of the week in a random sample of 140 births from local records in a large city. Do these data give significant evidence that local births are not equally likely on all days of the week?

  15. Age distribution of adults in California: 35% between 18 and 34 years old 51% between 35 and 64 years old 14% are 65 years or older Example 3: Who Buys Lotto Tix? In an SRS of 200 adults in California: 36 between 18 and 34 years old 130 between 35 and 64 years old 34 of those 65 years or older bought Lotto Tickets Do we have enough evidence to say that the age distributions of adults in CA are as stated?

  16. Drivers Rachel told Eric that the reason her car insurance is less expensive is that female drivers get in fewer accidents than male drivers. Specifically, she says that male drivers are held responsible in 65% of accidents involving drivers under 23. If Eric does some research of his own and discovers that 46 out of the 85 accidents he investigates involve male drivers, does his data support or refute Rachel’s hypothesis?

  17. Different Types of Chi-Square • Goodness of Fit (GOF) • One variable with multiple sub categories • Independence • More than one variable • “-----variable is associated with ------variable?” • Homogeneity • More than one variable • “----variable is the same as ------variable?

  18. Are fatal bicycle accidents equally likely throughout the 24-hour period of a day? Example 2:

  19. Inherited Traits Biologists wish to cross pairs of tobacco plants having genetic makeup Gg, indicating that each plant has one dominant gene (G) and one recessive gene (g) for color. Each offspring plant will receive one gene for color from each parent. The Punnett square suggests that the expected ratio of green (GG) to yellow-green (Gg) to albino (gg) tobacco plants should be 1:2:1. In other words, the biologists predict that 25% of the offspring will be green, 50% will be yellow-green, and 25% will be albino. To test their hypothesis about the distribution of offspring, the biologists mate 84 randomly selected pairs of yellow-green parent plants. Of 84 offspring, 23 plants were green, 50 were yellow-green, and 11 were albino. Do these data differ significantly from what the biologists have predicted? Carry out an appropriate test at the α = 0.05 level to help answer this question.

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