Chi-Square Goodness of Fit — Practice

Chi-Square Goodness of Fit — Practice. Practice questions to deepen understanding of the chi-square goodness of fit test. Online statistics practice with full solutions and step-by-step explanations.

Chi-square Goodness of Fit practice — comprehensive practice on the goodness of fit test, χ² computations, interpreting results.

30 questions

Question 1

3.33 pts

1:
more?

whether/is distribution categories distribution .

whether/is large .

whether/is mean .

whether/is variables .

Explanation:

equal mode mode , .

Question 2

3.33 pts

2:
?

variable distribution distribution .

variables .

mean .

when there are consecutive time measurements

Explanation:

variable , how many categories, whether/is mode .

Question 3

3.33 pts

3:
mode ?

category sample.

mode .

mean .

the variance of the groups

Explanation:

mode sample. how many , how many No.

Question 4

3.33 pts

4:
mode ?

the number of cases that would be expected in each category if the theoretical model is correct

mode .

mode No 100.

Explanation:

mode . , 100 categories equal, mode 25 category.

Question 5

3.33 pts

5:
?

sum over all categories of (O minus E) squared divided by E

O minus E .

sum of O times E

mean O E.

Explanation:

\( \chi^2 = \sum \frac{(O - E)^2}{E} \)
O mode E mode .

Question 6

3.33 pts

6:
k categories No parametric, how many ranks ?

k minus 1 ranks .

k ranks .

1 .

always 2.

Explanation:

No because parametric, ranks
\( df = k - 1 \).

Question 7

3.33 pts

7:
mode ?

categories mode 5.

categories mode 0.

categories mode equal.

categories small 3.

Explanation:

category, categories, mode No , No 5, distribution .

Question 8

3.33 pts

8:
?

All observations must be independent of each other.

The data must be normally distributed.

The expected frequencies must be at least 5 in each cell.

The sample size must exceed 100.

Explanation:

, . , .

Question 9

3.33 pts

9:
large ?

large mode , .

mode .

observed .

sample small Yes .

Explanation:

large O E large . .

Question 10

3.33 pts

The chart compares observed frequencies with expected frequencies in three categories. In which category does the gap between observed and expected appear largest?

category B

Category A

Category C

the gap is identical in all categories

Explanation:

category large observed , Yes large more .

Question 11

3.33 pts

11:
No ?

goodness-of-fit tests one categorical variable against a theoretical model; independence tests two categorical variables against each other

no difference — just a different name

goodness-of-fit tests linear correlation

normal distribution.

Explanation:

, variable , variables .

Question 12

3.33 pts

12:
p small ?

the observed distribution is far from the theoretical one, so there is evidence against the model

the model fits well

sample small .

equal No.

Explanation:

p small observed Correct small. Yes .

Question 13

3.33 pts

13:
p large ?

the observed distribution does not significantly contradict the model

the model is necessarily completely correct

the data are necessarily incorrect

equal mean.

Explanation:

p large because . .

Question 14

3.33 pts

14:
?

using percentages instead of absolute frequencies O and E

using variance instead of frequencies

mean mode.

category .

Explanation:

mode . No , .

Question 15

3.33 pts

15:
mode equal. . ?

Chi-square goodness-of-fit test.

Chi-square test of independence.

Mann-Whitney test.

Wilcoxon signed-rank test.

Explanation:

variable distribution equal. .

Question 16

3.33 pts

16:
Correct mode ?

mode equal mode .

mode large always .

mode always small 1.

mode 100.

Explanation:

sample, Yes O E .

Question 17

3.33 pts

17:
distribution calculate probability ?

mode sample large, distribution .

because always more normal.

because always categories.

because calculate.

Explanation:

distribution variables . , distribution distribution .

Question 18

3.33 pts

18:
categories mode ?

categories small ranks .

categories .

mode .

ranks .

Explanation:

categories mode , categories Yes ranks .

Question 19

3.33 pts

19:
calculate distribution?

because because large .

because because .

because .

because probability.

Explanation:

, Yes small . because large calculate H0.

Question 20

3.33 pts

20:
distribution . whether/is distribution ?

No. There are large deviations at values 2 and 4 relative to the uniform model

Yes. .

Yes. observed .

impossible to see anything from the diagram

Explanation:

equal category. categories , Yes distribution .

Question 21

3.33 pts

21:
?

distribution population distribution mode.

mean equal No.

equal 1.

variables .

Explanation:

H0 because distribution population . whether/is .

Question 22

3.33 pts

22:
H0 , ?

the true population distribution differs from the theoretical distribution being tested

the theoretical model is correct

no conclusion can be drawn

variables .

Explanation:

H0 observed large calculate , Yes .

Question 23

3.33 pts

23:
p large No H0?

writing that the model has been absolutely proven correct

writing that there is no possibility the model fits

writing that the data are completely random

sample No .

Explanation:

H0 Correct . sample given.

Question 24

3.33 pts

24:
because sample ?

sample large , sample small large No .

sample .

sample large .

sample small always .

Explanation:

sample large more, . always sample .

Question 25

3.33 pts

25:
distribution . ?

the probability of obtaining a test statistic at least as large as the observed value if H₀ is correct — this is the p-value

the sum of all probabilities

probability Correct .

probability sample small.

Explanation:

p . because more observed H0 .

Question 26

3.33 pts

26:
because ?

variable No calculate mode normal mode .

mean .

equal median 0.

whether/is categories.

Explanation:

categories, calculate category probability normal , sample E equal O .

Question 27

3.33 pts

27:
mode ?

the chi-square approximation will be weak and the p-value may be misleading

the test will stop working entirely and give no result

always .

No Yes .

Explanation:

E small , distribution . No categories .

Question 28

3.33 pts

28:
because categories ranks ?

more categories, ranks k minus 1.

more categories, ranks always.

categories .

ranks always equal 1.

Explanation:

ranks categories. more categories, more .

Question 29

3.33 pts

29:
because ?

the smaller alpha is, the harder it is to reject H₀ and a larger chi-square value is needed

more, more H0.

alpha has no effect at all

alpha determines the sample size

Explanation:

. , 0.01, because H0.

Question 30

3.33 pts

30:
?

checks how similar the actual data are to what the model predicts; the chi-square measure quantifies the total discrepancy

mean No categories.

checks only variance of continuous data

variables .

Explanation:

: Correct, . how many .