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Answered Same Day Aug 20, 2021


Bezawada Arun answered on Aug 22 2021
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Summer 2020 Week 11 Homework Questions
(Last updated 7/8/2020)
Chi Square
        Saeko has a yarn shop and wants to test her theory on what types of colors she is selling.
        She believes that Black, White, the Primary Colors, and Tertiary colors sell in equal amounts.
        The primary colors are blue, red, and yellow; while the tertiary colors are Brown, Green, and Purple.
        Test Saeko's theory using the 5 step hypothesis testing analysis and Chi Square at the .10 level of significance.
        Here is a pivot table that shows Saeko the number of yards that were sold in the various yarn types during the busiest weekend of her shop last year.
        Row Labels    Count of Color Type    Sum of Yards
        Black    23    35856
        Blue    16    17053
        Brown    13    13426
        Green    12    12509
        Purple    12    12131
        Red    8    8393
        White    26    37666
        Yellow    12    12874
        Grand Total    122    149908
    1)    Using the pivot table, fill in the blanks in the following table:
        Primary Colors consists of the sum of Blue, Red, and Yellow yarn sold
        Tertiary Colors consists of the sum of Brown, Green, and Purple Colors Sold.
        The Total in this chart must equal the Grand Total, Cell D19 in the above table.
            x    p    count    x*p(x)    (x-mean)^2*p(x)
        Black    35,856.00    0.2391867012    23    8,576.28    647,891.76
        White    37,666.00    0.2512607733    26    9,463.99    6,772.63
        Primary Colors    38,320.00    0.255623449    36    9,795.49    171,118.47
        Tertiary Colors    38,066.00    0.2539290765    37    9,666.06    80,824.98
        Total    149,908.00    1    122    37501.8214371481    906607.842598324
        This table represents the observed data in the Chi Square analysis.
        Find the Expected values for each of the colors. Saeko expects that the colors sell in equal amounts.
        Color Type    Sum of Yards
        Black    8,576.28
        White    9,463.99
        Primary Colors    9,795.49
        Tertiary Colors    9,666.06
        Total    37,501.82
         Subtract the Expected values from the observed values
        Color Type    Sum of Yards
        Black    27,279.72
        White    28,202.01
        Primary Colors    28,524.51
        Tertiary Colors    28,399.94
        Square the values just found
        Color Type    Sum of Yards
        Black    744,183,212.90
        White    795,353,464.71
        Primary Colors    813,647,638.36
        Tertiary Colors    806,556,351.96
        Divide each square by the expected value and add togethe
        Color Type    Sum of Yards
        Black    86,772.26
        White    84,039.97
        Primary Colors    83,063.50
        Tertiary Colors    83,442.10
        Total    337,317.83
    2)    This total is your Chi Square test statistic
        Use the 5 step hypothesis testing procedure to determine if Saeko's hypothesis that the colors sell in equal amounts is true.
        What is the null hypothesis?        There is no significant difference between the colors that sell in equal amounts
        What is the alternative hypothesis?        There is a significant difference between the colors that sell in equal amounts
        What is the level of significance?        0.10
    3)    What is the Chi Square test statistic?        337,317.83
    4)    What is the Chi Square critical Value?        Use =CHISQ.INV()
        What is your answer to Saeko?        State both the statstical answer (reject or do not reject, and what hypothesis), and also state your answer in English: What can Saeko learn from the data?
        Since the calculated value is greater than critical value
        Then we say that the alternative hypothesis is accepted.
        It can be infered that the data is not fit for the model
        Saeko owns a yarn shop and want to expands her color selection.
        Before she expands her colors, she wants to find out if her customers prefer one
        over another
and. Specifically, she is...

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