What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories?

Answer:The goodness of fitness test χ²with significance of level ∝= 0.05 and 5 degrees of freedom is 11.07  (One tailed test )Step-by-step explanation:For n=6  the degrees of freedom will be n-1 = 5 . The goodness of fitness test χ²with significance of level ∝= 0.05 and 5 degrees of freedom is 11.07  (One tailed test )The critical region depends on ∝ and the alternative hypothesis a) When Ha is σ²≠σ² the critical region is χ²  < χ²(1-∝/2)(n-1) and  χ² > χ²(1-∝/2)(n-1)   Two tailed test ( χ²  < 0.83) and ( χ²  > 0.83)b) When Ha is σ²> σ² the critical region falls in the right tail and its value is  χ² > χ²(∝)(n-1)   One tailed test  {11.07  (One tailed test )}c) When Ha is σ² <σ² the critical region will be entirely in the left tail with critical value   χ²(1-∝)(n-1)  One tailed test  (1.145)

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