Suppose that a response can fall into one of k -5 categories with probabilities

Question

Suppose that a response can fall into one of k -5 categories with probabilities pi, P2..... Ps and that n category counts. 300 re Category Observed Count 48 64 74 53 61 (a) Are the five categories equally likely to occur? How would you test this hypothesis? Ha: At least one p, is different from O Ho: At least one p; is different from 0 Ha: At least one p, is different from o H: At least one p, is different from 1 . At least one pi is different from (b) If you were to test this hypothesis using the chi-square statistic, how many degrees of freedom would the test have? degrees of freedom (c) Find the critical value of 2 that defines the rejection region with -0.05. (Round your answer to three decimal places.) 0.05 (d) Calculate the observed value of the test statistic. (Round your answer to two decimal places.) (e) Conduct the test and state your conclusions. 0 There is sufficient evidence to indicate that at least one category is more likely to occur than the others. O There is insufficient evidence to indicate that at least one category is more likely to occur than the others.

Explanation / Answer

(A) Here option A is correct about hypothesis question.

(B) Here degree of freedom = k -1 = 5 - 1= 4

critical value of chi-square

X20.05 = 9.488

(d) Here is the observed expecrted table with chi - square statistic

Here expected values ar e

Ei = (48 + 64 + 74 + 53 + 61)/5 = 60

X2 = (Oi -Ei)2/Ei

Here

X2 = 6.77

(e) Here as X2 < X2critical , there is insufficient evidence to say that at least one caregory is more likely to occur than the others.

Category Count Expected Chi 1 48 60 2.4 2 64 60 0.2667 3 74 60 3.2667 4 53 60 0.8167 5 61 60 0.0167 Sum 300 300 6.7667

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