Explain whether each of these is possible in a chisquare goo

Explain whether each of these is possible in a chi-square goodness-of-fit test.

1. The chi-square statistic is negative.

a. Yes

b. No   

2. A chi-square statistic is a sum of (a. non-negative) OR (b. negative numbers)so it would have to be (a. greater than or equal to) (b. greater than) (c. less than or equal to) (d. less than 0.)

3. The chi-square statistic is 0.

a. Yes

b. No   

4. This would happen if the observed count equaled the expected count in  ---Select---(a. less than two cells) (b. one of the cells) (c. each cell) of the table.

5. The expected counts are not whole numbers.

a. Yes

b. No

6. The expected count is a (a. actual count) (b. ratio) that is (a. never) (b. always) (c. sometimes) a whole number.

7. The observed counts are not whole numbers.

a. Yes

b. No   

8. The observed count is a (a. ratio) (b. actual count) that is (a. always) (b. sometimes) (c. never) a whole number.

9. The probabilities specified in the null hypothesis sum to less than 1.

a. Yes

b. No

10. The null hypothesis gives hypothesized probabilities for (a. most of) (b. the all) (c. some) possible categories so the sum of probabilities must be (a. less than equal to) (b. more than 1.)

11. The degrees of freedom are larger than the number of categories.

a. Yes

b. No   

For a goodness of fit test, df = (a. number of categories - 1) (b. number of categories) (c. number of categories + 1 ).

Solution

1. No. It is always positive as the numerator is squared (always positive) and the denominator is an expected frequency, which is also positive.

2.

A. non-negative
B. greater than or equal to 0.

[The smallest possible value of chi^2 is 0, that is, when ALL the observed values are exactly the expected ones.]

3. Possible, for the reason in #2.

4. C. Each cell, for the same reason.

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