Question

(1 pt) In each question below, we have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. In each case, decide whether the two assumptions for using that test are satisfied Assumption 1: All expected frequencies are 1 or greater Assumption 2: At most 20 percent of the expected frequencies are less than 5 Sample size: n 100, Relative frequencies: 0.65, 0.30, 0.05 A. Only assumption 1 is satisfied B. Both assumptions are satisfied C. Only assumption 2 is satisfied D. None of the assumptions are satisfied Sample size: n - 50, Relative frequencies: 0.22, 0.22, 0.25, 0.30, 0.01 A. Only assumption 2 is satisfied B. Only assumption 1 is satisfied C. Both assumptions are satisfied D. None of the assumptions are satisfied Sample size: n - 50, Relative frequencies: 0.22, 0.21, 0.25, 0.30, 0.02 A. Only assumption 1 is satisfied B. Both assumptions are satisfied C. Only assumption 2 is satisfied D. None of the assumptions are satisfied Sample size: n 100, Relative frequencies: 0.44, 0.25, 0.30, 0.01 A. Both assumptions are satisfied B. Only assumption 2 is satisfied O C. Only assumption 1 is satisfied D. None of the assumptions are satisfied

Answer 1

Following table shows the expected frequencies:

p	E=100*p
0.65	65
0.3	30
0.05	5

So both assumptions has been satisfied.

Correct option is B.

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Following table shows the expected frequencies:

p	E=50*p
0.22	11
0.22	11
0.25	12.5
0.3	15
0.01	0.5

Out of 5 expected frequencies, 1 is less than 5. That is 1/5 = 0.20 or 20% expected frequencies are less than 5.

Correct option is B.

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Following table shows the expected frequencies:

p	E=50*p
0.22	11
0.21	10.5
0.25	12.5
0.3	15
0.02	1

Out of 5 expected frequencies, 1 is less than 5. That is 1/5 = 0.20 or 20% expected frequencies are less than 5.

Correct option is B.

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Following table shows the expected frequencies:

p	E=100*p
0.44	44
0.25	25
0.3	30
0.01	1

Out of 4 expected frequencies, 1 is less than 5. That is 1/4 = 0.25 or 25% expected frequencies are less than 5.

Correct option is C.