I would like to know how to answer this questions. Please provide explanations.

Question

I would like to know how to answer this questions. Please provide explanations.

A multinomial experiment with 5 categories and 265 observations produced the data shown in the following table: The expected value for the category 2, to test that the categories are equally likely is: 53 56 0.169 None of the above The rejection region for the test of independence between 2 variables, for which the table contains 5 rows and 4 columns with a level of significance of 1% is: 36.5672 18.4753 26.2170 None of the above According to the following table, the test statistic to determine that the 2 variables A and B are not related, with a level of significance of 5% is:

Explanation / Answer

1) as all category are equally likely; hence expected value =265/5=53

2)here degree of freedom =(5-1)*(4-1)=12

hence for 0.01 level and 12 degree if freedom ; rejection region =26.217

3)

test stat =12.327

Observed O daily every other 2-3 /week Total northern 40 72 42 154 Southern 63 53 70 186 Southern 31 38 30 99 Total 134 163 142 439 Expected E=rowtotal*column total/grand total daily every other 2-3 /week Total northern 47.007 57.180 49.813 154 Southern 56.774 69.062 60.164 186 Southern 30.219 36.759 32.023 99 Total 134 163 142 439 chi square =(O-E)^2/E daily every other 2-3 /week Total northern 1.044 3.841 1.226 6.111 Southern 0.683 3.735 1.608 6.026 Southern 0.020 0.042 0.128 0.190 Total 1.747 7.618 2.961 12.327

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