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An Introduction to Statistics

Homework (in class) for Statistics Lesson 10

  1. Brian Small rolled a dice 1002 times and obtained the following results. Help him determine if the dice is fair by doing a chi square goodness of fit. Be sure to indicate your test statistic, tails, degrees of freedom, and critical test statistic.

    Pips:123456
    Observed181155141162153210
    Expected167167167167167167
    (Obs-Exp)           
    (O-E)2      
    (O-E)2/E      

     

     

  2. Indicate the value of any standardized residuals which are significant in problem 1.

     

  3. Susie Giavan got tired of rolling her die and made up the following data. Help her teacher test for data fabrication by doing a chi-square goodness of fit. Be sure to indicate all four steps and values in testing this hypothesis.

    Pips:123456
    Observed147157167162172195
    Expected167167167167167167
    (Obs-Exp)           
    (O-E)2      
    (O-E)2/E      

     

     

     

     

  4. Since 1995, blue M&M® candies replaced tan with 30% brown, 20% yellow, 20% red, 10% orange, 10% green, and 10% blue candies to be expected, on average. "While we mix the colors as thoroughly as possible, the above ratios may vary somewhat, especially in the smaller bags. This is because we combine the various colors in large quantities for the last production stage (printing). The bags are then filled on high-speed packaging machines by weight, not by count. Each student will obtain a random sample of 10 M&M's® from the common 14.0 oz bag. Then complete the table below.

    Color:BrownYellowRedOrangeGreenBlue
    Observed        
    Expected0.3n=___0.2n=___0.2n=___0.1n=___0.1n=___0.1n=___
    (O-E)2/E      

    Now add up the bottom row and call it 2. Compare your value with others. Did any particular color contribute significantly to this value?

     

     

     

     

  5. Bonus: After completing the count feel free to dispose of the M&M's® by any method you deem appropriate.

     

     

     

     

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