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. Find the x2 statistic to test the claim that the gym has equal numbers of members of all age ranges.
A
0.92
B
0.46
C
0.08
D
0.54
Verified step by step guidance1
Step 1: Calculate the total number of members surveyed by summing the values in the '# of Members' row. This will give the total sample size.
Step 2: Determine the expected frequency for each age group under the assumption that the gym has equal numbers of members across all age groups. Divide the total number of members by the number of age groups to find the expected frequency for each group.
Step 3: For each age group, calculate the difference between the observed frequency (given in the table) and the expected frequency. Square this difference to eliminate negative values.
Step 4: Divide the squared difference for each age group by the expected frequency. This step calculates the contribution of each age group to the chi-squared statistic.
Step 5: Sum all the contributions from Step 4 to find the chi-squared statistic (χ²). This value will be used to test the claim about equal distribution of members across age groups.
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