13. Chi-Square Tests & Goodness of Fit
Goodness of Fit Test
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A gym owner wants to know if the gym has similar numbers of members across different age groups. The table shows the distribution of ages for members from a random survey. Does this data set fit the criteria for a G.O.F. test?
A
Yes
B
No
C
More information is required.
Verified step by step guidance1
Step 1: Understand the problem. The gym owner wants to determine if the distribution of members across different age groups is similar. This requires a statistical test to compare observed frequencies (from the table) to expected frequencies.
Step 2: Recognize the type of test needed. A Goodness-of-Fit (G.O.F.) test is appropriate when you want to compare observed data to a theoretical distribution or expected frequencies. To decide if the data fits the criteria for a G.O.F. test, you need to check if expected frequencies are provided or can be calculated.
Step 3: Analyze the table. The table provides observed frequencies for five age groups: 18–25 (54 members), 26–35 (46 members), 36–45 (53 members), 46–55 (49 members), and 56+ (48 members). However, the table does not provide expected frequencies or a theoretical distribution to compare against.
Step 4: Determine if more information is required. To perform a G.O.F. test, you need expected frequencies or a theoretical distribution (e.g., uniform distribution, proportional distribution based on population demographics). Without this information, you cannot proceed with the test.
Step 5: Conclude. Based on the given data, the criteria for a G.O.F. test are not fully met because expected frequencies or a theoretical distribution are not provided. Therefore, the correct answer is 'More information is required.'
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