Stat 2470, Practice Final, Spring 2014
Supplementary Questions
Review previous exams and practice exams for Chapters 1-10, 12-13. These supplementary questions
only cover Chapter 14.
1. Which of the following statements are true regarding the critical value
for the chi-squared
distribution when
a. The area to the right of 9.488 is .05.
b. The area to the left of 9.488 is .95.
c. The total area under the chi-squared curve is 9.488.
d. All of the above statements are true.
e. None of the above statements are true.
2. Which of the following statements are true?
a. The
goodness-of-fit test can be used when the number of categories k is two or more.
b. If
, then
has a t distribution with one degree of freedom.
c. The chi-squared tests in this chapter are not all upper-tailed.
d. The P-value for an upper-tailed chi-squared test is the area under the chi-squared curve
with degrees of freedom to the left of the calculated test statistic value.
e. All of the above statements are true.
3. Which of the following statements are not true?
a. The chi-squared test statistic used in testing for independence is identical to that used in
testing for homogeneity.
b. In general, the number of degrees of freedom when testing for independence is larger
than those used in testing for homogeneity.
c. The chi-squared test for independence can safely be applied as long as the estimated
expected count
for all cells in the contingency table is larger than or equal to5.
d. The rejection region in testing for homogeneity at significance level is that the test
statistic value
where I and J are the number of rows and columns,
respectively, in the two-way contingency table.
e. All of the above statements are true.
4.
The number of degrees of freedom in testing for independence when using a contingency table
with 6 rows and 4 columns is:
a. 24
b. 10
c. 15
d. 20
e. 12
5. Say as much as you can about the P-value for an upper-tailed chi-squared test in each of the following
situations:
a.
b.
c.
d.
e.
6. A study focuses on the existence of any relationship between date of patient admission for treatment
of alcoholism and patient’s birthday. Assuming a 365-day year (i.e., excluding leap year), in the absence
of any relation, a patient’s admission date is equally likely to be any one of the 365 possible days. The
investigators established four different admission categories: (1) within 7 days of birthday, (2) between
8 and 30 days, inclusive, from the birthday, (3) between 31 and 90 days, inclusive, from the birthday, (4)
more than 90 days from the birthday. A sample of 200 patients gave observed frequencies of 11, 24, 69,
and 96 for categories 1, 2, 3, and 4, respectively. State and test the relevant hypotheses using a
significance level of .01.
ANS
1.
2.
3.
4.
5.
C
A
B
C
a. With d.f. = 2 , our
value of 8.15 falls between
value is between .01 and .025, or .01 <p-value<.025.
b. With d.f. = 6, our
value of 13.78 falls between
value < .05.
c. With d.f. = 9, our
value of 17.46 falls between
value <.05.
d. With k=5, d.f. = k-1= 4, and our
value of 19.92 exceeds
e.
With k=4, d.f. =k-1-3; and our
therefore the pso .025 < pso .025 < pso the p-value < .005.
value of 3.67 is less than
6.
so p-value > .10.
at least one proportion is not as stated in
The
degrees of freedom =3, and the rejection region is
Cell
Observed
Expected
1
11
2
24
3
69
4
96
8.22
25.21
65.75
100.82
.9402
.0581
.1606
.2304
which is not
, so
not rejected. The data does not indicate a relationship between patients’ admission date and birthday.
is