MATH 225N WEEK 7: STATISTICAL
REASONING - HYPOTHESIS TESTING,
CORRELATION, AND REGRESSION
QUESTIONS AND VERIFIED ANSWERS
|100% CORRECT| GRADE A+
1. Which of the following describes the Null Hypothesis (H0) in a statistical test?
A. A statement that there is a significant effect or relationship.
B. A statement of no effect, no difference, or the status quo.
C. A statement that the researcher hopes to prove true.
D. The probability of making a Type I error.
Answer: B
Conceptual Explanation: The null hypothesis (H0) is the assumption that no effect or
difference exists until evidence proves otherwise.
2. A researcher fails to reject the null hypothesis when the null hypothesis is actually false.
What has occurred?
A. Type II Error
B. Type I Error
C. Correct Decision
,D. Power of the Test
Answer: A
Conceptual Explanation: A Type II error (beta) occurs when a false null hypothesis is not
rejected.
3. If the P-value of a test is 0.024 and the significance level (alpha) is 0.05, what is the
appropriate conclusion?
A. Fail to reject the null hypothesis.
B. Accept the null hypothesis as true.
C. Reject the null hypothesis.
D. Increase the sample size to be sure.
Answer: C
Conceptual Explanation: If P is less than alpha (0.024 < 0.05), we reject the null
hypothesis.
4. Which test statistic should be used when testing a population mean when the population
standard deviation is unknown?
A. z-statistic
B. t-statistic
C. Chi-square statistic
D. F-statistic
, Answer: B
Conceptual Explanation: The t-distribution is used when the population standard
deviation (sigma) is unknown and replaced by the sample standard deviation (s).
5. What is the primary purpose of a scatterplot in regression analysis?
A. To determine the exact P-value of the intercept.
B. To calculate the standard error of the mean.
C. To visually inspect the relationship between two quantitative variables.
D. To verify that the null hypothesis is false.
Answer: C
Conceptual Explanation: Scatterplots allow researchers to see the direction, form, and
strength of a relationship between two variables.
6. A correlation coefficient of r = -0.85 indicates what kind of relationship?
A. Weak positive linear relationship
B. Strong positive linear relationship
C. Strong negative linear relationship
D. Weak negative linear relationship
Answer: C
REASONING - HYPOTHESIS TESTING,
CORRELATION, AND REGRESSION
QUESTIONS AND VERIFIED ANSWERS
|100% CORRECT| GRADE A+
1. Which of the following describes the Null Hypothesis (H0) in a statistical test?
A. A statement that there is a significant effect or relationship.
B. A statement of no effect, no difference, or the status quo.
C. A statement that the researcher hopes to prove true.
D. The probability of making a Type I error.
Answer: B
Conceptual Explanation: The null hypothesis (H0) is the assumption that no effect or
difference exists until evidence proves otherwise.
2. A researcher fails to reject the null hypothesis when the null hypothesis is actually false.
What has occurred?
A. Type II Error
B. Type I Error
C. Correct Decision
,D. Power of the Test
Answer: A
Conceptual Explanation: A Type II error (beta) occurs when a false null hypothesis is not
rejected.
3. If the P-value of a test is 0.024 and the significance level (alpha) is 0.05, what is the
appropriate conclusion?
A. Fail to reject the null hypothesis.
B. Accept the null hypothesis as true.
C. Reject the null hypothesis.
D. Increase the sample size to be sure.
Answer: C
Conceptual Explanation: If P is less than alpha (0.024 < 0.05), we reject the null
hypothesis.
4. Which test statistic should be used when testing a population mean when the population
standard deviation is unknown?
A. z-statistic
B. t-statistic
C. Chi-square statistic
D. F-statistic
, Answer: B
Conceptual Explanation: The t-distribution is used when the population standard
deviation (sigma) is unknown and replaced by the sample standard deviation (s).
5. What is the primary purpose of a scatterplot in regression analysis?
A. To determine the exact P-value of the intercept.
B. To calculate the standard error of the mean.
C. To visually inspect the relationship between two quantitative variables.
D. To verify that the null hypothesis is false.
Answer: C
Conceptual Explanation: Scatterplots allow researchers to see the direction, form, and
strength of a relationship between two variables.
6. A correlation coefficient of r = -0.85 indicates what kind of relationship?
A. Weak positive linear relationship
B. Strong positive linear relationship
C. Strong negative linear relationship
D. Weak negative linear relationship
Answer: C
