Deck 20: Chi-Square and Inference About Frequencies

Question 1

You wish to see if consumers differ in their preference for three different fast-food restaurants. You conduct a survey with 60 subjects and obtain the following frequencies for preference: restaurant A = 30, restaurant B = 18, and restaurant C = 12. Compute X²
and perform the test at ( $\alpha$ = .05).

Answer 1

Question 2

In a comprehensive review of past real estate sales, researchers noted that even though four styles of homes were offered to potential home buyers with equal frequency, the actual number of purchases of each type of home were slightly different. There were 2,144 homes purchased. Do the observed frequencies indicate any preference for particular styles? Use
$\alpha$ = .05
(a) Colonial: 514 purchased
(b) Cape Cod: 498 purchased
(c) Victorian: 604 purchased
(d) Salt Box: 528 purchased

Answer 2

Question 3

In a poll taken 3 months ago, the preferences of voters among three candidates running for mayor were: Smith = 45%, Jones = 35%, and Thompson = 20%. Candidate Thompson's election committee has just polled 120 likely voters at random and found that 40 said that they would vote for Smith, 35 for Jones and 45 for Thompson. Has the voter's preference changed since the earlier poll [use ( $\alpha$ = .05)]?

Answer 3

Question 4

Each of a sample of 100 participants at a weekend workshop responds to a particular attitude statement as follows:
(a) State (in words) the null hypothesis of independence for this situation in terms of proportions.
(b)Compute the expected frequencies under the null hypothesis of independence.
(c)Complete the X² and draw final conclusions.
(d)Translate each obtained frequency into a proportion based on its row frequency. What interpretation seems likely?

Question 5

A random sample of registered voters is selected from each of the three major areas of a western city. Those in the samples are asked for their preferences among three candidates for mayor.
(a)State (in words) the null hypothesis of independence for this situation in terms of proportions.
(b)Perform the $X^2$ test of independence $(\alpha = .05)$ and draw conclusions.
(c)Do your results from (b) prove that voter preference is unrelated to area of the city? Explain.

Question 6

The basic element of chi-square is

A)
B)
C)
D)

Question 7

The obtained values of chi-square

A) can be negative if discrepancies have negative values
B) can be negative even if no discrepancy is negative
C) can be no lower than zero
D) cannot be as low as zero

Question 8

We wish to test the null hypothesis that students guess at random on a particular 4-alternative multiple-choice item. The choices for a random sample of 24 students are:

The value of f_e for alternative (2) is

A) 9
B) 7
C) 5
D) 6

Question 9

Only red and blue flowers are produced from a particular seed mixture. We plant a random sample of 27 seeds and obtain 6 blue and 21 red flowers. We wish to test the null hypothesis that the mixture gives twice as many red flowers as blue flowers. The value of f_e for red flowers is

A) 18
B) 16
C) 9
D) 13 1/2

Question 10

For a particular category, we find the difference between expected and observed frequency to differ by 25 points. This will tend to make chi-square large if

A) the difference is positive
B) the difference is negative
C) f_e is small
D) f_o is small

Question 11

In one chi-square problem, each observed frequency was the same as its expected frequency.

A) This would be an unusual even if the null hypothesis were true.
B) This would be an unusual even if the null hypothesis were false.
C) Chi-square will be zero.
D) All of the above are true.

Question 12

In the chi-square test, we will reject the null hypothesis if the obtained chi-square is

A) very low
B) very high
C) either very low or very high
D) close to the mean of the tabled distribution of chi-square

Question 13

In the chi-square test, a very low (close to 0) value of chi-square implies that

A) the observed frequencies are more like their corresponding expected frequencies than would be expected by chance
B) the several observed frequencies are very similar
C) the several expected frequencies are very similar
D) the positive difference between expected and observed frequencies tend to balance the negative differences

Question 14

For a given level of significance, the critical value of chi-square will be larger

A) when n is larger
B) when the number of degrees of freedom is smaller
C) when the number of degrees of freedom is larger
D) when the number of categories is smaller

Question 15

In a chi-square goodness-of-fit problem, there are 6 categories, and expected frequencies of 5 in each category. The number of degrees of freedom for this problem is

A) 5
B) 24
C) 25
D) 29

Question 16

The chi-square distribution is like the t distribution in that

A) its mean is zero
B) it is actually a family of distributions
C) it is symmetrical
D) both positive and negative values are possible

Question 17

Which, if any, is not a characteristic necessary for obtained values of chi-square to be distributed according to the tabled values of the chi-square distribution?

A) expected frequencies must be equal for all groups
B) the null hypothesis must be true
C) sampling must be random
D) all of the above must be true

Question 18

when

A) both are normally distributed
B)
C)
D)

Question 19

Older texts recommended using a "correction for continuity" when ,
particularly if f_e in one of the categories was less than 5. However, more recent studies have shown that the uncorrected chi-square is reasonably accurate when

A) all f_e's are at least 2
B) all f_e's are at least 3
C) the average f_e is at least 2
D) the average f_e is at least 5

Question 20

We want to know whether the proportion of freshman men who select psychology as their major differs from the proportion of freshman women who do so. This question may be tested by

A) the chi-square test for the one-variable case
B) the t test of the difference between two means
C) the chi-square test of independence
D) either (a) or (b) will work

Question 21

Chi-square analysis of a contingency table provides the answer to the question

A) is there a difference among the categories of a variable?
B) is there a difference among the categories of one variable, and also among categories of a second variable?
C) is there a relationship between two variables?
D) are the categories of one variable the same as those of the other variable?

Question 22

The contingency table is a form of

A) frequency distribution
B) relative frequency distribution
C) cumulative frequency distribution
D) bivariate frequency distribution

Question 23

In chi-square analysis of the contingency table, the null hypothesis is that

A) the categories of at least one of the two variables do not differ from expectation
B) the categories of both variables do not differ from expectation
C) there is no relation between classification according to category in one variable
D) each of the above is tested by the null hypothesis

Question 24

In a contingency table, the number of degrees of freedom is

A) R * C
B) (R+C) - 1
C) RC - 1
D) (R - 1)(C - 1)

Question 25

Use the following data to answer Questions


-The number of degrees of freedom for this problem is

A) 199
B) 5
C) 4
D) 2

Question 26

Use the following data to answer Questions


-The expected frequency for the upper right cell on the hypothesis of independence is

A) 20
B) 25
C) 30
D) not determinable for the information given

Question 27

Use the following data to answer Questions


-The observed frequency for the upper right cell is

A) 20
B) 25
C) 30
D) not determinable from the information given