131 141 Chi Square Goodness Of Fit

When to use the Chi Square, χ 2 , Procedure ,[object Object],[object Object]

This Chapter will Cover Three Tests based on the Chi-square Distributions. ,[object Object],[object Object],[object Object]

Required Conditions For Goodness of Fit Procedure ,[object Object],[object Object],[object Object],[object Object],[object Object]

Hypothesizes for Goodness of Fit Test ,[object Object],[object Object]

Chi-square Test Statistic Degree of freedom = k – 1, where k is the number of categories. Use the appropriate chi-square distribution based on degree of freedom, to find the critical value of χ 2 at an α level.

Properties of Chi-square Distributions ,[object Object],[object Object],[object Object]

Example 1 ,[object Object],From the Motor Vehicle Bureau records, we select a random sample of 1,000 of new car purchases for one of these four types of foreign cars in the current year. The information is displayed below: Frequency Is the current year’s sales distribution the same as last year’s sales ? 37% Honda 35% Toyota 10% Mazda 18% Nissan 400 Honda 385 Toyota 65 Mazda 150 Nissan

Example 1 Continued ,[object Object],[object Object],[object Object],[object Object],[object Object]

Example 1 Continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 1 Continued ,[object Object],Observed Expected Count (O) Count (E) Sum = 23.18 From Table D using df = 3 and α = 0.05, the critical χ 2 * = 7.81. 2.43 370 400 Honda 3.50 350 385 Toyota 12.25 100 65 Mazda 5 180 150 Nissan

Example 1 Continued ,[object Object],[object Object],[object Object]

Example 2 ,[object Object],[object Object],[object Object],[object Object]

Example 2 Continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 2 continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 2 Continued ,[object Object],Use calculator. L1 = Observed counts L2 = Expected counts L3 – (O –E) 2 /E = (L1 – L2) 2 / L2 Sum (L3) Sum = χ 2 2 nd Distr χ 2 cdf( Lower bound, Upper bound, df)

Example 2 Continued ,[object Object],[object Object],[object Object]

131 141 Chi Square Goodness Of Fit

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