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Use Scenario 11-1. To answer the question posed above about car color and speeding tickets, the appropriate
null hypothesis is:
The distribution of car colors for the speeding citations is the same as the distribution of
colors for cars on the highway.
Use Scenario 11-1. Which of the following are the correct expected counts for speeding tickets under the null
hypothesis?
red- 16.8
Use Scenario 11-1. The chi-square statistic for this test is
8.461 with 3 degrees of freedom, which yields a
P-value of 0.037. Which of the following is an appropriate conclusion to draw?
Reject H0 at the = 0.05 level: there is evidence that certain car colors get more speeding
tickets than others.
Use Scenario 11-2. For this test, the
2
statistic has approximately a chi-square (
2
) distribution. How many
degrees of freedom does this distribution have?
3
Use Scenario 11-2. Which of the following is the component of the
2
statistic corresponding to the category
"less than 2"?
(18-25)²/25
Use Scenario 11-2. The value of the
2 statistic is found to be 3.03. The P-value of the test is
A. greater than 0.20.
greater than 0.20.
Which of the following statements is true of chi-square distributions?
They take on only positive values.
Which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test?
The expected count for each category is greater than 5.
Use Scenario 11-3. Which of the following conditions must be met before the reporter can use the
2
procedure in this situation??
Each observation was randomly selected from the population of all grades given by the
new teacher.
Use Scenario 11-3. Assuming that the
2 statistic has approximately a
2
distribution, how many degrees of
freedom does the distribution have?
4
Use Scenario 11-3. Which of the following expressions represents the expected count of the grade category
D?
(.10)(90)
Use Scenario 11-3. The grade category that contributes the largest component to the
2
statistic is
D
Use Scenario 11-3. The computed value of the
2 statistic for the reporter's test is 6.074, which produces a
P-value of 0.1937. Which of the following is an appropriate conclusion?
Fail to reject H0: there is insufficient evidence from the test to conclude that the grade
distribution of the new teacher is different from that of other teachers.
Which of the following statements is not true about chi-square distributions?
The mean decreases as the degrees of freedom increase.
If each observed count is exactly equal to each expected count in a chi-square goodness-of-fit test, then the
chi-square statistic will
equal 0.
A statistics teacher wants to know if the proportion of students at his school that are born in certain months is
different from the proportion born in other months. He uses school records to determine the birth month of
all the students at the school and calculates a chi-square statistic to test the null hypothesis that the proportion
born in each month matches the proportion of days of the year that are in each month. Why is this not an
appropriate use of a chi-square goodness-of-fit test?
Since his population of interest is his school, he has taken a census, not a sample.
Use Scenario 11-4. Ida decides to perform a chi-square goodness-of-fit test to see if there is a significant
difference in the brand of cookie people prefer.
The proportion of people at the school who prefer each brand of cookie is 0.25.
Use Scenario 11-4. The brand category that contributes the largest component to the
2
statistic is
B
Use Scenario 11-5. The conditional distribution for preferred cookie brand among males (in percents) is given
by which of the following?
A: 11%; B: 16%; C: 34%; D: 39%
Use Scenario 11-5. If we want to compare the conditional distributions for preferred cookie brand among
males to the same distribution for females, which of the following is an appropriate graph to use?
Side-by-side histograms
Scenario 11-5. The appropriate null hypothesis for Ida's question in this problem is:
Gender and cookie brand are independent.
Use Scenario 11-5. The expected count for the cell "Males/Brand B" cell is given by which of the following
expressions?
(38)(18)/96
Use Scenario 11-6. The chi-square statistics for this test would have a
2
distribution with how many degrees
of freedom?
2
Use Scenario 11-6. The conditional distribution of the variable "Wear Glasses" for Average readers (in
percents) is:
38.1%; 61.9%
Use Scenario 11-6. Suppose we wish to test the null hypothesis that there is no association between the
amount of reading you do and whether or not you wear glasses. Under the null hypothesis, which of the
following is the expected number (approximately) of above-average readers who wear glasses?
30.7
Use Scenario 11-6. Suppose we wished to display in a graph the proportion of all above-average readers who
wear glasses and do not wear glasses, respectively. Which of the following graphical displays is best suited to
this purpose?
A bar graph
Which of the following statements is supported by the information in this table and the original two-way
table?
Most of the below-average readers did not wear glasses.
Use Scenario 11-7. Suppose we wish to test the null hypothesis that the proportion of subsequent arrests is the
same regardless of the treatment assigned. Which of the following statements is true?
We cannot test this hypothesis because the expected cell counts are less than 5 in some of
the cells.
The cell that contributes most to the
2
statistic is
Americans in the Northeastern United States who complained.
Use Scenario 11-8. The appropriate degrees of freedom for the
2
statistic is
2
Use Scenario 11-8. Which of the following intervals contains the P-value of the test?
larger than 0.20.
Use Scenario 11-8. Which of the following may we conclude, based on the test results?
There is not much evidence of an association between wiring configuration and the type of
cancer that caused the deaths of children in the study.
Use Scenario 11-9. Which hypotheses are being tested by a chi-square test on these data?
The null hypothesis is that the distribution of whether or not a student is strongly opposed
is the same for each of the four years. The alternative is that the distribution is different for
at least two of the four years.
Use Scenario 11-9. Which of the following are conditions that must be met before performing a chi-square
test on these data?
II only
Use Scenario 11-10. Which of the following are appropriate null and alternative hypotheses for these data?
Ho: There is no association between hand dominance and allergies.
H-a: There is an association between hand dominance and allergies.
Use Scenario 11-10. Which expression below represents the expected count for left-handed students with
allergies?
(20)(118)/200
Use Scenario 11-11. The chi-square statistic for this test is
2
= 11.239. Which of the following is the correct
conclusion to draw?
Reject H0 at = 0.05; fail to reject H0 at = 0.01.
Use Scenario 11-11. Which of the following are appropriate null and alternative hypotheses for these data?
Ho: The distribution of favorite food group is the same for both genders.
Ha: The distribution of favorite food group is not the same for both genders.
Use Scenario 11-11. Which of the following cells contributions the most to the chi-square statistic?
Male/Proteins
Use Scenario 11-11. Which of the following represents the individual component of chi-square contributed by
the cell Female/Dairy?
(20-21.2)²/21.2
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