,MATH 110 Module 7 Exam - Introduction to
Statistics Portage Learning - Latest (26/27)
1. In hypothesis testing, the null hypothesis is a statement about which of the following?
A) The sample statistic
B) The population parameter
C) The sample size
D) The test statistic
Correct Answer: B) The population parameter
Rationale: The null hypothesis is a statement about a population parameter, such as the population
mean or proportion. It is not about a sample statistic, sample size, or test statistic. The sample statistic
is used to test the claim about the parameter, making it the correct focus of the null hypothesis.
2. The alternative hypothesis in a hypothesis test represents:
A) The claim that the null hypothesis is true
B) The claim that the researcher wants to provide evidence for
C) The probability of making a Type I error
D) The sample mean
Correct Answer: B) The claim that the researcher wants to provide evidence for
Rationale: The alternative hypothesis is the claim that the researcher is trying to find evidence for,
and it contradicts the null hypothesis. The null hypothesis is the claim to be tested, and the
probability of a Type I error is denoted by α. The sample mean is a statistic, not a hypothesis.
3. A Type I error in hypothesis testing is defined as:
A) Rejecting the null hypothesis when it is true
B) Failing to reject the null hypothesis when it is false
,C) Rejecting the alternative hypothesis when it is true
D) Failing to reject the alternative hypothesis when it is false
Correct Answer: A) Rejecting the null hypothesis when it is true
Rationale: A Type I error occurs when the null hypothesis is true, but we incorrectly reject it. Failing to
reject a false null hypothesis is a Type II error. The other options reverse the definitions or are not
standard error types in hypothesis testing.
4. A Type II error in hypothesis testing is defined as:
A) Rejecting the null hypothesis when it is true
B) Failing to reject the null hypothesis when it is false
C) Rejecting the alternative hypothesis when it is false
D) Failing to reject the alternative hypothesis when it is true
Correct Answer: B) Failing to reject the null hypothesis when it is false
Rationale: A Type II error occurs when the null hypothesis is false, but we fail to reject it. Rejecting a
true null hypothesis is a Type I error. The other options do not accurately describe a Type II error in
the context of hypothesis testing.
5. The significance level (α) of a hypothesis test is the probability of:
A) Making a Type II error
B) Making a Type I error
C) The test statistic being greater than the critical value
D) The p-value being greater than 0.05
Correct Answer: B) Making a Type I error
, Rationale: The significance level α is the probability of making a Type I error (rejecting a true null
hypothesis). It is set by the researcher before conducting the test. The probability of a Type II error is
β, and the p-value is compared to α for decision-making.
6. If a hypothesis test results in a p-value of 0.03 and α = 0.05, what decision should be made?
A) Reject the null hypothesis
B) Fail to reject the null hypothesis
C) Reject the alternative hypothesis
D) Accept the null hypothesis
Correct Answer: A) Reject the null hypothesis
Rationale: If the p-value is less than α (0.03 < 0.05), the result is statistically significant, and the null
hypothesis is rejected. Failing to reject occurs when p ≥ α. We never "accept" the null hypothesis as
true; we either reject it or fail to reject it.
7. If a hypothesis test results in a p-value of 0.08 and α = 0.05, what decision should be made?
A) Reject the null hypothesis
B) Fail to reject the null hypothesis
C) Reject the alternative hypothesis
D) Accept the null hypothesis
Correct Answer: B) Fail to reject the null hypothesis
Rationale: If the p-value is greater than or equal to α (0.08 ≥ 0.05), the result is not statistically
significant, and we fail to reject the null hypothesis. Rejecting occurs when p < α. The decision is never
to "accept" the null hypothesis.
8. A one-tailed test is used when:
A) The alternative hypothesis is two-sided
B) The alternative hypothesis specifies a direction (greater than or less than)
Statistics Portage Learning - Latest (26/27)
1. In hypothesis testing, the null hypothesis is a statement about which of the following?
A) The sample statistic
B) The population parameter
C) The sample size
D) The test statistic
Correct Answer: B) The population parameter
Rationale: The null hypothesis is a statement about a population parameter, such as the population
mean or proportion. It is not about a sample statistic, sample size, or test statistic. The sample statistic
is used to test the claim about the parameter, making it the correct focus of the null hypothesis.
2. The alternative hypothesis in a hypothesis test represents:
A) The claim that the null hypothesis is true
B) The claim that the researcher wants to provide evidence for
C) The probability of making a Type I error
D) The sample mean
Correct Answer: B) The claim that the researcher wants to provide evidence for
Rationale: The alternative hypothesis is the claim that the researcher is trying to find evidence for,
and it contradicts the null hypothesis. The null hypothesis is the claim to be tested, and the
probability of a Type I error is denoted by α. The sample mean is a statistic, not a hypothesis.
3. A Type I error in hypothesis testing is defined as:
A) Rejecting the null hypothesis when it is true
B) Failing to reject the null hypothesis when it is false
,C) Rejecting the alternative hypothesis when it is true
D) Failing to reject the alternative hypothesis when it is false
Correct Answer: A) Rejecting the null hypothesis when it is true
Rationale: A Type I error occurs when the null hypothesis is true, but we incorrectly reject it. Failing to
reject a false null hypothesis is a Type II error. The other options reverse the definitions or are not
standard error types in hypothesis testing.
4. A Type II error in hypothesis testing is defined as:
A) Rejecting the null hypothesis when it is true
B) Failing to reject the null hypothesis when it is false
C) Rejecting the alternative hypothesis when it is false
D) Failing to reject the alternative hypothesis when it is true
Correct Answer: B) Failing to reject the null hypothesis when it is false
Rationale: A Type II error occurs when the null hypothesis is false, but we fail to reject it. Rejecting a
true null hypothesis is a Type I error. The other options do not accurately describe a Type II error in
the context of hypothesis testing.
5. The significance level (α) of a hypothesis test is the probability of:
A) Making a Type II error
B) Making a Type I error
C) The test statistic being greater than the critical value
D) The p-value being greater than 0.05
Correct Answer: B) Making a Type I error
, Rationale: The significance level α is the probability of making a Type I error (rejecting a true null
hypothesis). It is set by the researcher before conducting the test. The probability of a Type II error is
β, and the p-value is compared to α for decision-making.
6. If a hypothesis test results in a p-value of 0.03 and α = 0.05, what decision should be made?
A) Reject the null hypothesis
B) Fail to reject the null hypothesis
C) Reject the alternative hypothesis
D) Accept the null hypothesis
Correct Answer: A) Reject the null hypothesis
Rationale: If the p-value is less than α (0.03 < 0.05), the result is statistically significant, and the null
hypothesis is rejected. Failing to reject occurs when p ≥ α. We never "accept" the null hypothesis as
true; we either reject it or fail to reject it.
7. If a hypothesis test results in a p-value of 0.08 and α = 0.05, what decision should be made?
A) Reject the null hypothesis
B) Fail to reject the null hypothesis
C) Reject the alternative hypothesis
D) Accept the null hypothesis
Correct Answer: B) Fail to reject the null hypothesis
Rationale: If the p-value is greater than or equal to α (0.08 ≥ 0.05), the result is not statistically
significant, and we fail to reject the null hypothesis. Rejecting occurs when p < α. The decision is never
to "accept" the null hypothesis.
8. A one-tailed test is used when:
A) The alternative hypothesis is two-sided
B) The alternative hypothesis specifies a direction (greater than or less than)
