Deck 7: Hypothesis Testing With Nominal and Ordinal Variables: CHI Square

Question 1

A null hypothesis of "no association" is rejected at the 0.01 level. Which of the following is a valid conclusion?

A) The null hypothesis is not true.
B) The odds are 1 to 1 that the correct decision has been made.
C) The odds are 10 to 1 that the correct decision has been made.
D) The odds are 100 to 1 that the correct decision has been made.

Answer 1

The odds are 100 to 1 that the correct decision has been made.

Question 2

A teacher wants to determine if students who use a new study method improve their performance. Which of the following would be the best example of a null hypothesis used to formally test this idea?

A) Students using the new study method do no better than the typical class average.
B) Students using the new study method do at least 3× better than other students in the course.
C) Students using the new study method do any amount better than other students in the course.
D) The odds of students using the new method improving their marks are at least 5 to 1.

Answer 2

Students using the new study method do no better than the typical class average.

Question 3

If an observed test statistic is within the "critical region," what should we conclude?

A) The mean for a sample is different from the mean of the population.
B) It falls in an area of the sampling distribution that includes unlikely sample outcomes.
C) There is likely "no difference" or "no relationship" between the variables.
D) It falls near the centre of the sampling distribution.

Answer 3

It falls in an area of the sampling distribution that includes unlikely sample outcomes.

Question 4

What may be concluded if the test statistic falls in the critical region in a test of significance?

A) The research hypothesis is true.
B) The population distribution is normal.
C) The sample size was too small.
D) The null hypothesis can be rejected.

Question 5

If a null hypothesis that is in fact true has been rejected, then which of the following is indicated?

A) A Type II error has been made.
B) A correct decision has been made.
C) A one-tailed test should have been used.
D) A Type I error has been made.

Question 6

When a researcher chooses alpha, what is he or she essentially selecting the probability of?

A) committing a Type I error
B) committing a Type II error
C) the null hypothesis being correct
D) the null hypothesis being incorrect

Question 7

What is the alpha level at which a researcher would most likely reject the null hypothesis?

A) 0.001
B) 0.01
C) 0.05
D) 0.10

Question 8

Which of the following is a researcher more likely to do at a higher alpha level?

A) commit a Type II error
B) conduct a two-tailed test
C) reject the null hypothesis
D) commit a Type I error

Question 9

What is the assumed sampling distribution for a chi square test?

A) the F distribution
B) the t distribution
C) the Z distribution
D) The chi square test makes no assumption about the sampling distribution.

Question 10

Suppose that both variables in a bivariate table have four categories. How many cells will the table have?

A) 16
B) 8
C) 4
D) 2

Question 11

Which of the following is an example of a polytomous variable that could be depicted in a bivariate table?

A) working for an employer versus being self-employed
B) proportion of lifetime months spent working at present job
C) working versus self-employed versus retired versus unemployed
D) proportion of weekly hours spent at work

Question 12

A researcher analyzes data from a bivariate table with a chi square test. The two variables in the table are sex (man, woman) and political affiliation (NDP, Liberal, Conservative). What does the null hypothesis state?

A) Sex causes people's political affiliation.
B) Sex and political affiliation are dependent.
C) Sex and political affiliation are independent.
D) Women are more likely to vote than men.

Question 13

Which of these terms refers to cell frequencies computed under the assumption that the null hypothesis is true?

A) expected frequencies
B) observed frequencies
C) random frequencies
D) null frequencies

Question 14

A chi square test concludes that home owners and home renters differed in their likelihood of having a registered retirement savings plan (RRSP). What would characterize the expected and observed frequencies of these variables in the bivariate table?

A) Observed frequencies are basically equivalent to expected frequencies.
B) Observed frequencies differ greatly from expected frequencies.
C) Observed frequencies are positive, and expected frequencies are negative.
D) Observed frequencies exceed marginal totals.

Question 15

Which of the following would summarize the relationship between f_e (expected frequencies) and f_o (observed frequencies) if we reject the null hypothesis in a chi square test?

A) f_e = f_o
B) f_e is very similar to f_o.
C) f_e is much greater than f_o, but not that f_o is much greater than f_e.
D) f_e is much greater than f_o or f_o is much greater than f_e.

Question 16

If row marginal = 75, column marginal = 12, and n = 50, what is the expected frequency?

A) 1.74
B) 18
C) 180
D) 850

Question 17

The observed row and column marginals of a bivariate table are 22 and 40 respectively. What can be concluded about the total expected values for the rows and columns?

A) They must also be 22 and 40.
B) They must be greater than the observed frequencies.
C) They must be less than the observed frequencies.
D) They must be exactly half the value of the observed marginals.

Question 18

How are degrees of freedom computed for a chi square test?

A) n₁ + n₂ - 2
B) n - 1
C) (r - 1)(c - 1)
D) (r + 1)(c + 1)

Question 19

Where would the critical region begin for a chi square test with the alpha level set at 0.05 and with 8 degrees of freedom?

A) at 2.73
B) at 11.07
C) at 15.51
D) at 58.30

Question 20

How is the shape of sampling distribution for chi square different from that of the Z and the t distributions?

A) Chi square has a mode at the left and at the right side of its distribution.
B) Chi square is negatively skewed.
C) Chi square is positively skewed.
D) They are all actually identical in their general shape.

Question 21

A researcher wishes to compare criminal defendants from three self-reported social classes (lower, middle, and upper) on the outcomes of their criminal trial (guilty vs. innocent). What would be the degrees of freedom for conducting a chi square test?

A) 2
B) 3
C) 6
D) 12

Question 22

In a research study conducted to determine whether owning a pet was related to high life satisfaction, the chi square critical score was 3.84 and the chi square test statistic was 28.5. Which of the following can be concluded from these results?

A) The probability of getting these results by random chance alone is 0.5.
B) Pet ownership causes higher life satisfaction.
C) The variables are independent.
D) The variables are dependent.

Question 23

An obtained chi square of 9.53 was calculated and the critical chi square was 18.48. What should be concluded from these results?

A) The information is incomplete; nothing can be concluded.
B) The variables are independent.
C) The null hypothesis must be rejected.
D) The result is both statistically significant and important.

Question 24

What does "significance" mean in the statistical sense?

A) The difference detected in a hypothesis test is strong enough to have important implications in the real world.
B) The probability of Type I and Type II errors has been adequately estimated to ensure that the test is informative.
C) The difference between a sample statistic and population parameter is unlikely to occur by random chance alone.
D) The sample used is large enough to be informative about the general population.

Question 25

When should the Yates correction for continuity be used?

A) in 5 × 5 tables when degrees of freedom are >25
B) in 2 × 2 tables when degrees of freedom are <5
C) in 2 × 2 tables when any expected cell counts are <5
D) in tables of any size when the critical value exceeds the degrees of freedom

Question 26

A researcher reports a ÷² (obtained) of 67.14 (á = 0.05, df = 2, ÷² (critical) = 3.84, n = 16,987). The researcher claims that the relationship is statistically significant. Which of these issues should be raised?

A) The sample size is very large; therefore, the actual relationship between the variables might be trivial.
B) The value for ÷² (critical) is much too low.
C) The degrees of freedom are much too small for a sample this large.
D) The test is using an unconventional alpha level.

Question 27

-Refer to the table. Which of the following is a valid marginal value?

A) 7
B) 9
C) 26
D) 35

Question 28

-Refer to the table. The column percentages from this table tell us that what percent of female newborns have low birth weight?

A) (7/86) × 100 = 8.14%
B) (9/85) × 100 = 10.58%
C) (7/50) × 100 = 14%
D) (7/16) × 100 = 43.75%

Question 29

Briefly describe what Type I errors and Type II errors are and how they are related.

Question 30

In your own words, define and explain each of the following terms and concepts.
a. null hypothesis
b. Type I (alpha) error
c. sampling distribution

Question 31

A university has implemented a training program to educate incoming students about the problem of sexual assault on campus. A sample of students was selected from the new student population and tested for whether they thought the instructor taught the material effectively. Are instructor evaluations related to a student's program of study? Using the five-step model and an alpha level of 0.05, write a sentence or two interpreting your results.
Evaluation Major Total
Social Sciences Sciences/
Engineering Business
Instructor taught very well 36 23 17 76
Instructor taught adequately 20 17 16 53
Instructor taught poorly 10 18 36 64
Total 66 58 69 193