MATH 225N WEEK 6: STATISTICAL
REASONING - HYPOTHESIS TESTING &
CONFIDENCE INTERVALS QUESTIONS
AND VERIFIED ANSWERS |100%
CORRECT| GRADE A+
1. A researcher wants to test the claim that the average weight of a specific breed of dog is
more than 50 pounds. What is the correct alternative hypothesis (Ha)?
A. Ha: μ > 50
B. Ha: μ < 50
C. Ha: μ = 50
D. Ha: μ ≠ 50
Answer: A
Conceptual Explanation: The alternative hypothesis represents the claim being tested.
Since the claim is ‘more than 50’, the mathematical representation is μ > 50.
2. If a researcher rejects the null hypothesis when the null hypothesis is actually true, what
type of error has occurred?
A. Sampling Error
B. Type II Error
,C. Standard Error
D. Type I Error
Answer: D
Conceptual Explanation: A Type I error occurs when the null hypothesis is rejected even
though it is true (a false positive).
3. What is the probability of committing a Type I error denoted by?
A. Beta (β)
B. Alpha (α)
C. Power
D. Confidence Level
Answer: B
Conceptual Explanation: Alpha (α) is the significance level, representing the maximum
probability of committing a Type I error.
4. A test has a p-value of 0.023. If the significance level α is 0.05, what is the correct decision?
A. Fail to reject the null hypothesis
B. Reject the null hypothesis
C. Accept the null hypothesis
D. Increase the sample size
, Answer: B
Conceptual Explanation: If the p-value is less than or equal to α, the null hypothesis is
rejected. 0.023 < 0.05.
5. In a two-tailed test, the null hypothesis is Ho: μ = 100. If the test statistic is z = 2.10, what
can be said about the p-value compared to a one-tailed test with the same z-score?
A. The p-value is the same
B. The p-value is doubled
C. The p-value is halved
D. The p-value is zero
Answer: B
Conceptual Explanation: In a two-tailed test, the area in both tails is summed, making the
p-value twice that of a one-tailed test for the same statistic.
6. Which of the following is the correct formula for the z-test statistic for a mean when the
population standard deviation is known?
A. z = (μ - x̄ ) / (σ / ∑n)
B. z = (x̄ - μ) / (σ / ∑n)
C. z = (x̄ - μ) / (s / ∑n)
D. z = (x̄ - μ) / σ
Answer: B
REASONING - HYPOTHESIS TESTING &
CONFIDENCE INTERVALS QUESTIONS
AND VERIFIED ANSWERS |100%
CORRECT| GRADE A+
1. A researcher wants to test the claim that the average weight of a specific breed of dog is
more than 50 pounds. What is the correct alternative hypothesis (Ha)?
A. Ha: μ > 50
B. Ha: μ < 50
C. Ha: μ = 50
D. Ha: μ ≠ 50
Answer: A
Conceptual Explanation: The alternative hypothesis represents the claim being tested.
Since the claim is ‘more than 50’, the mathematical representation is μ > 50.
2. If a researcher rejects the null hypothesis when the null hypothesis is actually true, what
type of error has occurred?
A. Sampling Error
B. Type II Error
,C. Standard Error
D. Type I Error
Answer: D
Conceptual Explanation: A Type I error occurs when the null hypothesis is rejected even
though it is true (a false positive).
3. What is the probability of committing a Type I error denoted by?
A. Beta (β)
B. Alpha (α)
C. Power
D. Confidence Level
Answer: B
Conceptual Explanation: Alpha (α) is the significance level, representing the maximum
probability of committing a Type I error.
4. A test has a p-value of 0.023. If the significance level α is 0.05, what is the correct decision?
A. Fail to reject the null hypothesis
B. Reject the null hypothesis
C. Accept the null hypothesis
D. Increase the sample size
, Answer: B
Conceptual Explanation: If the p-value is less than or equal to α, the null hypothesis is
rejected. 0.023 < 0.05.
5. In a two-tailed test, the null hypothesis is Ho: μ = 100. If the test statistic is z = 2.10, what
can be said about the p-value compared to a one-tailed test with the same z-score?
A. The p-value is the same
B. The p-value is doubled
C. The p-value is halved
D. The p-value is zero
Answer: B
Conceptual Explanation: In a two-tailed test, the area in both tails is summed, making the
p-value twice that of a one-tailed test for the same statistic.
6. Which of the following is the correct formula for the z-test statistic for a mean when the
population standard deviation is known?
A. z = (μ - x̄ ) / (σ / ∑n)
B. z = (x̄ - μ) / (σ / ∑n)
C. z = (x̄ - μ) / (s / ∑n)
D. z = (x̄ - μ) / σ
Answer: B
