13. Chi-Square Tests & Goodness of Fit
Goodness of Fit Test
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A marketing associate for a supermarket chain wants to determine how many of each snack type to stock. According to previous market research, customers' preferences tend to follow the distribution in the table. If approximately 200 snack items are purchased in a day, what is the expected frequency of each snack type?
A
18, 11, 6, 8, 12
B
36, 21, 12, 8, 23
C
40, 40, 40, 40, 40
D
72, 42, 24, 16, 46
Verified step by step guidance1
Step 1: Understand the problem. The goal is to calculate the expected frequency of each snack type based on the given preference percentages and the total number of snack items purchased in a day (200).
Step 2: Identify the preference percentages for each snack type from the table: Chips (36%), Cookies (21%), Crackers (12%), Nuts (8%), and Granola Bars (23%).
Step 3: Convert the percentages into decimal form by dividing each percentage by 100. For example, Chips: 36% = 0.36, Cookies: 21% = 0.21, and so on.
Step 4: Multiply the decimal form of each preference percentage by the total number of snack items purchased (200). For example, for Chips: 0.36 × 200 = expected frequency for Chips.
Step 5: Repeat the multiplication for each snack type to calculate the expected frequency for Cookies, Crackers, Nuts, and Granola Bars. This will give the expected frequency for all snack types.
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