Goodness of fit a marketer is planning to introduce a

Goodness of Fit
• A marketer is planning to introduce a new product to the market but she is
not sure about the color of the package the product should be sold in. To
know if consumers have a preference in terms of color of packaging she
conducts a pilot experiment using an alpha level of .05. The number of
products sold for each color is provided in the chart below:
Color Blue Green Red Yellow
# Sold 30 20 35 15

Goodness of Fit
• H
0
: the population proportions are equal
• H
a
: the population proportions are not equal
Color Blue Green Red Yellow
# Expected
# Sold
25
30
25
20
25
35
25
15

2

Test of Independence
• We want to know if the column variable is independent of the
row variable.
– H
0
: the column variable is independent of the row variable
– H
a
: the column variable is not independent of the row variable
• How does it work?
– Select a random sample and record the observed frequencies for each
cell
– Compute the expected frequency for each cell
– Compute the test statistic using the difference between the expected
frequency and observed frequency in each category

Test of Independence
• 𝑒
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