In a matched pairs design, two measurements are taken on the same subject or on two closely matched subjects.
Correct Answer
True
True. Pairing links each measurement in one condition to a specific measurement in the other, either by using the same person twice or by matching similar people. The analysis then works with the difference within each pair.
Category: Matched Pairs
Question 2
Scores of the same 20 students on a pretest and a posttest form two independent samples.
Correct Answer
False
False. Each student contributes both scores, so the two sets of scores are paired, not independent. The correct analysis is a matched pairs t test on the 20 differences.
Category: Choosing the Test
Question 3
In a test of two independent means, the null hypothesis is often written H0: mu1 - mu2 = 0.
Correct Answer
True
True. A null hypothesis of no difference says the two population means are equal, which is the same as saying their difference is zero. The alternative then says the difference is positive, negative, or not zero.
Category: Writing Hypotheses
Question 4
The two-sample t test for independent means requires both population standard deviations to be known.
Correct Answer
False
False. The two-sample t test is used when the population standard deviations are unknown, and the sample standard deviations s1 and s2 take their place. When both sigmas are known, a two-sample z test is used instead.
Category: Comparing Two Means
Question 5
In a two-proportion z test, the null hypothesis states that the two population proportions are equal.
Correct Answer
True
True. The null hypothesis is H0: pA = pB, which can also be written pA - pB = 0. The alternative states that the proportions differ or that one is larger.
Category: Writing Hypotheses
Question 6
The standard error of the difference between two independent sample means is found by adding the two standard deviations.
Correct Answer
False
False. For independent samples the variances of the sample means add, so the standard error is sqrt(s1^2/n1 + s2^2/n2). Simply adding standard deviations overstates the spread and ignores the sample sizes.
Category: Comparing Two Means
Question 7
The Aspin-Welch t test does not assume that the two population standard deviations are equal.
Correct Answer
True
True. The Aspin-Welch test keeps the two sample variances separate in the standard error and adjusts the degrees of freedom, so it remains valid when the population standard deviations differ.
Category: Comparing Two Means
Question 8
In a two-proportion z test, the test statistic follows Student's t distribution.
Correct Answer
False
False. The test statistic for a difference in proportions follows an approximately normal distribution, so it is a z-score. Student's t distribution is used for means when the standard deviations are estimated.
Category: Comparing Two Proportions
Question 9
The two-sample t test uses the sample standard deviations s1 and s2 in place of the unknown population standard deviations.
Correct Answer
True
True. Since sigma1 and sigma2 are unknown, they are estimated by s1 and s2 in the standard error. That extra estimation is why the t distribution is used instead of the standard normal.
Category: Comparing Two Means
Question 10
A Cohen's d of 0.5 is conventionally described as a small effect.
Correct Answer
False
False. By Cohen's conventions, 0.5 is a medium effect. A small effect is about 0.2 and a large effect is about 0.8.
Category: Effect Size
Question 11
A study comparing the mean test scores of randomly chosen students at two different colleges uses two independent samples.
Correct Answer
True
True. The students at one college have no link to the students at the other, so the samples are independent. A two-sample test for independent means fits this design.
Category: Choosing the Test
Question 12
In a matched pairs test with 10 pairs, the test statistic has 19 degrees of freedom.
Correct Answer
False
False. A matched pairs test analyzes one sample of 10 differences, so it has 10 - 1 = 9 degrees of freedom. The value 19 wrongly counts all 20 measurements.
Category: Matched Pairs
Question 13
In a matched pairs test, the null hypothesis usually states that the population mean of the differences is 0.
Correct Answer
True
True. If the treatment or condition has no effect, the differences should average zero in the population, so H0: mu_d = 0. The alternative states that mu_d is positive, negative, or not zero.
Category: Matched Pairs
Question 14
A two-proportion z test is the right tool when the same people answer a yes or no question before and after a treatment.
Correct Answer
False
False. The two-proportion z test requires independent samples, but answers from the same people before and after are paired. Data like these need a method designed for paired responses.
Category: Comparing Two Proportions
Question 15
Comparing the proportion of left-handed people in two separate random samples calls for a two-proportion z test.
Correct Answer
True
True. Each person either is or is not left-handed, and the two samples are independent, so the comparison is between two population proportions. The two-proportion z test is designed for this situation.
Category: Choosing the Test
Question 16
The alternative Ha: mu1 - mu2 > 0 makes the same claim as the alternative Ha: mu2 - mu1 > 0.
Correct Answer
False
False. Ha: mu1 - mu2 > 0 claims the first mean is larger, while Ha: mu2 - mu1 > 0 claims the second mean is larger. Reversing the order of subtraction reverses the direction of the claim.
Category: Writing Hypotheses
Question 17
With p-hatA = 0.30 and p-hatB = 0.25, the observed difference p-hatA - p-hatB is 0.05.
Correct Answer
True
True. The difference in sample proportions is 0.30 - 0.25 = 0.05. In a two-proportion z test, this observed difference is compared with the hypothesized difference, usually 0, and divided by the standard error.
Category: Comparing Two Proportions
Question 18
If s1^2/n1 = 4 and s2^2/n2 = 5, the standard error of x-bar1 - x-bar2 is 9.
Correct Answer
False
False. The standard error is the square root of the sum: sqrt(4 + 5) = sqrt(9) = 3. The value 9 is the variance of the difference, not its standard error.
Category: Comparing Two Means
Question 19
Cohen's d uses a pooled standard deviation that combines the two sample standard deviations.
Correct Answer
True
True. Cohen's d divides the difference in sample means by a pooled standard deviation computed from both samples, weighted by their degrees of freedom. The result expresses the difference in standard deviation units.
Category: Effect Size
Question 20
A two-sample t test for independent means requires the two samples to be the same size.
Correct Answer
False
False. The two-sample t test works with unequal sample sizes, because the standard error uses each sample's own size, as in sqrt(s1^2/n1 + s2^2/n2). Equal sizes are convenient but not required.
Category: Comparing Two Means