The alternative hypothesis never contains an equal sign.
Correct Answer
True
True. The alternative uses less than, greater than, or not equal to, while the equality belongs to the null hypothesis. This is why a test can reject the null value in favor of a range of other values.
Category: Setting Up Hypotheses
Question 2
Failing to reject the null hypothesis proves that the null hypothesis is true.
Correct Answer
False
False. Not rejecting H0 only means the sample did not give enough evidence against it. The null could still be false, which is exactly the situation of a Type II error.
Category: P-Values and Decisions
Question 3
Whether a test is left-tailed, right-tailed, or two-tailed is determined by the alternative hypothesis.
Correct Answer
True
True. A less-than alternative gives a left-tailed test, a greater-than alternative gives a right-tailed test, and a not-equal alternative gives a two-tailed test. The null hypothesis alone does not decide the direction.
Category: Setting Up Hypotheses
Question 4
Concluding that a null hypothesis is false when it is actually true is called a Type II error.
Correct Answer
False
False. Rejecting a true null hypothesis is a Type I error. A Type II error is failing to reject a null hypothesis that is actually false.
Category: Type I and II Errors
Question 5
A Type II error can occur only when the null hypothesis is false.
Correct Answer
True
True. A Type II error means not rejecting H0 when H0 is false, so it is possible only when the null is false. When H0 is true, the only possible error is a Type I error.
Category: Type I and II Errors
Question 6
The p-value is the probability that the null hypothesis is true.
Correct Answer
False
False. The p-value is calculated assuming H0 is true; it is the probability of getting a sample result at least as extreme as the one observed. It does not measure how likely H0 itself is.
Category: P-Values and Decisions
Question 7
When alpha is greater than the p-value, the decision is to reject the null hypothesis.
Correct Answer
True
True. A p-value below alpha means the observed result would be rare enough under H0 to count as evidence against it. When the p-value is greater than or equal to alpha, H0 is not rejected.
Category: P-Values and Decisions
Question 8
A smaller p-value gives weaker evidence against the null hypothesis.
Correct Answer
False
False. A smaller p-value means the observed result would be less likely if H0 were true, so it gives stronger evidence against H0. A large p-value gives weak evidence against H0.
Category: P-Values and Decisions
Question 9
For a one-sample t test of a mean, the degrees of freedom equal the sample size minus 1.
Correct Answer
True
True. A one-sample t test uses df = n - 1 because the sample standard deviation is computed from n deviations that must sum to zero. For example, a sample of 10 gives 9 degrees of freedom.
Category: Choosing the Distribution
Question 10
In a left-tailed test, the p-value is the area to the right of the test statistic.
Correct Answer
False
False. In a left-tailed test, the p-value is the area to the left of the test statistic, because values farther left are more extreme in the direction of the alternative. The area to the right is used for a right-tailed test.
Category: P-Values and Decisions
Question 11
A test statistic measures how far the sample result lies from the value stated in H0, in units of standard error.
Correct Answer
True
True. A z or t statistic subtracts the hypothesized value from the sample statistic and divides by the standard error. A large value in either direction signals a result far from what H0 predicts.
Category: Test Statistic Calculations
Question 12
Lowering the significance level from 0.05 to 0.01 makes a Type I error more likely.
Correct Answer
False
False. The significance level is the probability of a Type I error, so lowering it from 0.05 to 0.01 makes a Type I error less likely. The trade-off is a greater chance of a Type II error when the sample size stays the same.
Category: Type I and II Errors
Question 13
In a hypothesis test, the hypotheses should be stated before the sample data are collected.
Correct Answer
True
True. The null and alternative hypotheses are set up first, and the data are then gathered to decide between them. Choosing hypotheses after seeing the data would let the data shape the question being tested.
Category: Setting Up Hypotheses
Question 14
Rejecting a null hypothesis that is actually false is a Type I error.
Correct Answer
False
False. Rejecting a false null hypothesis is a correct decision. A Type I error is rejecting a null hypothesis that is actually true.
Category: Type I and II Errors
Question 15
If a test statistic falls in the rejection region, the p-value is smaller than alpha.
Correct Answer
True
True. The rejection region is built so that its total probability under H0 equals alpha. A test statistic beyond the cutoff therefore has a tail probability, its p-value, that is less than alpha.
Category: P-Values and Decisions
Question 16
A right-tailed test is used when the alternative hypothesis contains a less-than sign.
Correct Answer
False
False. A less-than sign in the alternative gives a left-tailed test. A right-tailed test is used when the alternative contains a greater-than sign.
Category: Setting Up Hypotheses
Question 17
A p-value of 0.04 is statistically significant at alpha = 0.05 but not at alpha = 0.01.
Correct Answer
True
True. At alpha = 0.05 the p-value of 0.04 is below the cutoff, so H0 is rejected. At alpha = 0.01 the p-value is above the cutoff, so H0 is not rejected.
Category: P-Values and Decisions
Question 18
With sigma = 10 and n = 25, the standard error of the sample mean is 0.4.
Correct Answer
False
False. The standard error is sigma / sqrt(n) = 10 / 5 = 2. The value 0.4 comes from dividing sigma by n instead of by the square root of n.
Category: Test Statistic Calculations
Question 19
The null hypothesis is the claim assumed to be true when the p-value is computed.
Correct Answer
True
True. The p-value is the probability of a result at least as extreme as the observed one under the assumption that H0 is true. The test then asks whether the data are surprising enough to reject that assumption.
Category: Setting Up Hypotheses
Question 20
A one-sample t test of a mean requires that the population standard deviation be known.
Correct Answer
False
False. The t test is used precisely when the population standard deviation is unknown, and the sample standard deviation s takes its place. When sigma is known, a z test is used instead.
Category: Choosing the Distribution