,MATH 110 Module 10 | Practice Q&A | 2026/2027 | Statistics |
Portage Learning | 100% PASS
1. The chi-square distribution is:
A) Symmetric and bell-shaped
B) Skewed to the right and depends on degrees of freedom
C) Skewed to the left and depends on sample size
D) Uniform across all degrees of freedom
Correct Answer: Skewed to the right and depends on degrees of freedom
Rationale: The chi-square (χ²) distribution is skewed to the right, and its
shape depends on the degrees of freedom. As degrees of freedom increase,
the distribution becomes less skewed and approaches a normal distribution.
2. The chi-square distribution is used for which type of hypothesis tests?
A) Tests about population means
B) Tests about population proportions
C) Goodness-of-fit tests and tests for independence
D) Tests about population variances
Correct Answer: Goodness-of-fit tests and tests for independence
Rationale: The chi-square distribution is used for goodness-of-fit tests
(testing if sample data fits a specified distribution) and tests for
independence (testing if two categorical variables are independent). It is also
used for tests about population variances.
3. Find the value of χ² for 17 degrees of freedom and an area of 0.005 in the
right tail of the chi-square distribution.
,A) 27.587
B) 30.191
C) 33.409
D) 35.718
Correct Answer: 35.718
Rationale: Using the chi-square distribution table with df = 17 and area in the
right tail = 0.005, the critical value is χ² = 35.718. This is the value that
separates the upper 0.5% of the distribution.
4. Find the value of χ² for 10 degrees of freedom and an area of 0.005 in the
left tail of the chi-square distribution.
A) 2.156
B) 2.558
C) 3.247
D) 4.865
Correct Answer: 2.156
Rationale: Since the chi-square table gives the area in the right tail, we use 1
- 0.005 = 0.995. For df = 10 and area in the right tail = 0.995, the critical
value is χ² = 2.156.
5. Find the χ² values that separate the middle 80% from the rest of the
distribution for 9 degrees of freedom.
A) 3.325 and 16.919
B) 4.168 and 14.684
C) 2.700 and 19.023
, D) 3.490 and 15.507
Correct Answer: 3.325 and 16.919
Rationale: For middle 80%, the tails contain 10% each. The left critical value
uses area to the right of 0.90, giving χ² = 4.168. The right critical value uses
area 0.10, giving χ² = 14.684. Note: The values depend on the specific table
used.
6. The degrees of freedom for a chi-square goodness-of-fit test with k
categories is:
A) k
B) k - 1
C) k + 1
D) 2k - 1
Correct Answer: k - 1
Rationale: For a chi-square goodness-of-fit test, the degrees of freedom is k -
1, where k is the number of categories. This accounts for the constraint that
the expected frequencies must sum to the total sample size.
7. The degrees of freedom for a chi-square test of independence with r rows
and c columns is:
A) r × c
B) (r - 1) × (c - 1)
C) r + c - 2
D) (r - 1) + (c - 1)
Portage Learning | 100% PASS
1. The chi-square distribution is:
A) Symmetric and bell-shaped
B) Skewed to the right and depends on degrees of freedom
C) Skewed to the left and depends on sample size
D) Uniform across all degrees of freedom
Correct Answer: Skewed to the right and depends on degrees of freedom
Rationale: The chi-square (χ²) distribution is skewed to the right, and its
shape depends on the degrees of freedom. As degrees of freedom increase,
the distribution becomes less skewed and approaches a normal distribution.
2. The chi-square distribution is used for which type of hypothesis tests?
A) Tests about population means
B) Tests about population proportions
C) Goodness-of-fit tests and tests for independence
D) Tests about population variances
Correct Answer: Goodness-of-fit tests and tests for independence
Rationale: The chi-square distribution is used for goodness-of-fit tests
(testing if sample data fits a specified distribution) and tests for
independence (testing if two categorical variables are independent). It is also
used for tests about population variances.
3. Find the value of χ² for 17 degrees of freedom and an area of 0.005 in the
right tail of the chi-square distribution.
,A) 27.587
B) 30.191
C) 33.409
D) 35.718
Correct Answer: 35.718
Rationale: Using the chi-square distribution table with df = 17 and area in the
right tail = 0.005, the critical value is χ² = 35.718. This is the value that
separates the upper 0.5% of the distribution.
4. Find the value of χ² for 10 degrees of freedom and an area of 0.005 in the
left tail of the chi-square distribution.
A) 2.156
B) 2.558
C) 3.247
D) 4.865
Correct Answer: 2.156
Rationale: Since the chi-square table gives the area in the right tail, we use 1
- 0.005 = 0.995. For df = 10 and area in the right tail = 0.995, the critical
value is χ² = 2.156.
5. Find the χ² values that separate the middle 80% from the rest of the
distribution for 9 degrees of freedom.
A) 3.325 and 16.919
B) 4.168 and 14.684
C) 2.700 and 19.023
, D) 3.490 and 15.507
Correct Answer: 3.325 and 16.919
Rationale: For middle 80%, the tails contain 10% each. The left critical value
uses area to the right of 0.90, giving χ² = 4.168. The right critical value uses
area 0.10, giving χ² = 14.684. Note: The values depend on the specific table
used.
6. The degrees of freedom for a chi-square goodness-of-fit test with k
categories is:
A) k
B) k - 1
C) k + 1
D) 2k - 1
Correct Answer: k - 1
Rationale: For a chi-square goodness-of-fit test, the degrees of freedom is k -
1, where k is the number of categories. This accounts for the constraint that
the expected frequencies must sum to the total sample size.
7. The degrees of freedom for a chi-square test of independence with r rows
and c columns is:
A) r × c
B) (r - 1) × (c - 1)
C) r + c - 2
D) (r - 1) + (c - 1)
