Module 10 Flashcards
The test of the difference between two means differs from the test of a hypothesis about a single mean with regard to A) Logic of the test B) Choice of level of significance C) The H₀ to be tested D) None of the above
C) The H₀ to be tested
Two sample groups are treated differently and then compared with regard to their performance on a test of short term memory. Statistical hypothesis testing would be used here to
A) Decide whether a difference would remain when the effects of sampling error are ruled out
B) Determine if the population difference is large enough to be of importance
C) Determine whether the sample difference is of statistical importance
D) Eliminate the effects of chance factors from the sample results.
A) Decide whether a difference would remain when the effects of sampling error are ruled out
The Hypothesis H₁: µA - µB < 0 is the same as: A) H₁: µA > µB B) H₁: µA ≠ µB C) H₁: µA < µB D) None of the above
D) None of the above
Suppose that X₁ and X₂ stand for scores on a test of learning under conditions of reward and punishment, respectively. If we are interested only in whether reward results in higher scores than punishment, and obtain the difference between the two conditions in terms of (x̄₁ - x̄₂), we should place the region of rejection:
A) Entirely in the right tail of the sampling distribution
B) Entirely in the left tail of the sampling distribution
C) Half in one tail and half in the other
D) In the center of the sampling distribution
A) Entirely in the right tail of the sampling distribution
The hypothesis testing procedures for comparing means of independent samples would be inappropriate for comparing
A) Achievement scores of a sample taught by method A with those of a sample taught by method B
B) Coordination scores of a sample of volunteers on the first trial with their scores on the second trial
C) Sociability scores of a sample of psychology majors with those of a sample of sociology majors
D) Maze running scores of a sample of albino rats with those of a sample of Norwegian rats
B) Coordination scores of a sample of volunteers on the first trial with their scores on the second trial
In testing a hypothesis about the difference between two means, the probability of rejecting H₀ (when there is a difference) is increased when A) n₁ > n₂ B) n₂ > n₁ C) Both n₁ and n₂ are small D) Both n₁ and n₂ are large
D) Both n₁ and n₂ are large
The formula for the standard error of the difference between means (independent samples) can be written as: A) √(σ₁²/n₁ - σ₂²/n₂) B) √(σ₁²/n₁ + σ₂²/n₂) C) √(σ₁² + (σ₂²/n₂) + n₁) D) √(σ₁² - (σ₂²/n₂) - n₁)
B) √(σ₁²/n₁ + σ₂²/n₂)
Suppose that in fact µ₁ = 60 and µ₂ = 65. The mean of a sampling distribution of x̄₁ - x̄₂ for samples drawn from these populations would equal: A) +5 B) 0 C) -5 D) Can't tell from the information given
C) -5
The size of the standard error of the different between means does not depend on: A) µ₁ and µ₂ B) σ₁ and σ₂ C) n₁ and n₂ D) s₁ and s₂
A) µ₁ and µ₂
Samples of size 12 and 10 are selected from populations 1 and 2 respectively. The sample results give SS₁ = 112 and SS₂ = 78. Our best pooled estimate of σ₁ and σ₂ is: A) 8.6 B) 9.5 C) 17.1 D) 12.2
B) 9.5
A variance estimate is computed from: A) Sample means B) Population variances C) Sample differences D) Sums of squared deviations
D) Sums of squared deviations
The scores from two randomly selected samples from populations A and B are as follows:
A: 2, 4 B: 3, 5
The pooled variance estimate, s₂pooled, would equal: A) 1 B) 2 C) 3 D) 4
B) 2
The variance estimate made by pooling data from two samples is calculated by:
A) SS₁ / (n₁ - 1) + SS₂ / (n₂ - 1)
B) 0.50 [SS₁ / (n₁ - 1) + SS₂ / (n₂ - 1)]
C) (SS₁ + SS₂) / (n₁ + n₂)
D) (SS₁ + SS₂) / (n₁ + n₂ - 2)
D) (SS₁ + SS₂) / (n₁ + n₂ - 2)
Sums of squared deviations and degrees of freedom are used to arrive at:
A) Sampling distributions of differences between means
B) Population standard deviations
C) t ratios
D) Variance estimates
D) Variance estimates
We wish to test the hypothesis of no difference between the means of two independent samples. The first sample consists of 30 cases and the second consists of 20 cases. The number of degrees of freedom for the test is A) 25 B) 48 C) 49 D) 50
B) 48
The difference between testing a hypothesis about 2 means and testing a hypothesis about a single mean lies in:
A) The appropriate probability distribution (normal vs. Student’s t)
B) The level of significance (α)
C) The relative merit of a one- or two-tailed test
D) None of the above
D) None of the above
To test the hypothesis of no difference between two means, we calculate the statistic: A) (x̄₁ - x̄₂) / s(x̄₁ - x̄₂) B) (x̄₁ - x̄₂) / s(x̄₁ - x̄₂) C) (x̄₁ - x̄₂) / √(sx̄₁ - x̄₂) D) (x̄₁ - x̄₂) / sx̄₁ + sx̄₂
B) (x̄₁ - x̄₂) / s(x̄₁ - x̄₂)
Samples of size 8 and 6 respectively are used to test H₀: µ₁ - µ₂ = 0 against H₁: µ₁ - µ₂ ≠ 0 using α = 0.01. The critical values of t for this test would be: A) 2.624 B) 3.055 C) 3.012 D) 2.681
B) 3.055
Samples of size 3 and 7 respectively are used to test H₀: µ₁ - µ₂ = 0 against H₁: µ₁ - µ₂ > 0 using α = 0.10. The critical values of t for this test would be: A) 1.383 B) 1.860 C) 1.372 D) 1.397
D) 1.397
Professor Jones performs a t test of H₀: µ₁ - µ₂ = 0 using α = 0.01 and finds a significant difference between x̄₁ and x̄₂. From this we can infer:
A) A large difference between µ₁ and µ₂
B) An important difference between µ₁ and µ₂
C) µ₁ and µ₂ to be unequal
D) All of the above
C) µ₁ and µ₂ to be unequal
An unimportant difference can turn out to be statistically significant because of:
A) Violations of the assumptions underlying the t test
B) Large population standard deviations
C) Use of deviation scores rather than raw scores
D) Large sample sizes
D) Large sample sizes
The difference between two sample means is found to be significant using α = 0.01. The sample means are x̄₁ = 154 and x̄₂ = 146, and s(pooled) = 40. We would estimate the true difference to be A) Small B) Moderate C) Large D) Very large
A) Small
In establishing a confidence interval for the difference between two means, selecting a confidence level of 0.95 rather than a confidence level of 0.90 implies that:
A) We can be less sure that the interval contains the true difference
B) The interval will be wider
C) The difference between the two sample means will be less
D) The difference between the two population means will be greater
B) The interval will be wider
The rule for constructing an interval estimate of the difference between two means is:
A) (µ₁ - µ₂) ± tαs(x̄₁ - x̄₂)
B) tα ± (x̄₁ - x̄₂) s(x̄₁ - x̄₂)
C) (x̄₁ + tαs(x̄₁ - x̄₂)) + (x̄₂ + tαs(x̄₁ - x̄₂))
D) (x̄₁ - x̄₂) ± tαs(x̄₁ - x̄₂)
D) (x̄₁ - x̄₂) ± tαs(x̄₁ - x̄₂)
A 95% confidence interval for the difference between µ₁ and µ₂ runs from –2 to +6. From this we can infer that:
A) µ₁ is probably greater than µ₂
B) µ₁ is probably less than µ₂
C) There may be no difference at all between µ₁ and µ₂
D) The difference between µ₁ and µ₂ is not very large in any case
C) There may be no difference at all between µ₁ and µ₂
With the same data we might contemplate testing a hypothesis or constructing an interval estimate. The number of degrees of freedom for these two procedures will differ
A) If the situation involves a single mean
B) If the situation involved two independent means
C) If the situation involves a one-tailed test
D) None of the above
D) None of the above
A 95% confidence interval for µ₁ - µ₂ is computed from a pair of random samples. The interval runs from –2 to +4. The difference between the sample means must have been: A) 1 B) 2 C) 3 D) Can’t tell from what is given
A) 1
Suppose a 95% confidence interval for µ₁ - µ₂ runs from –10 to –2. It appears likely that: A) µ₁ > µ₂ B) µ₁ < µ₂ C) µ₁ ≠ µ₂ D) µ₁ = µ₂
B) µ₁ < µ₂
Which factor will not affect the width of a confidence interval constructed to estimate the difference between two population means? A) x̄₁ - x̄₂ B) The size of s₁ and s₂ C) The size of n₁ and n₂ D) The level of confidence
A) x̄₁ - x̄₂
Suppose a 95% confidence interval for µ₁ - µ₂ runs from –5 to +2. If H₀: µ₁ - µ₂ = 0 were tested against a two-tailed alternative using α = 0.05, our decision about H₀:
A) Is uncertain
B) Should be to reject H₀
C) Should be to retain H₀
D) Cannot be determined without further information
C) Should be to retain H₀
Suppose a 95% confidence interval for µ₁ - µ₂ runs from –10 to –2. If H₀: µ₁ - µ₂ = 0 were tested against a two-tailed alternative using α = 0.05, our decision about H₀:
A) Is uncertain
B) Should be to reject H₀
C) Should be to retain H₀
D) Cannot be determined without further information
B) Should be to reject H₀
A factor that can play a crucial role in the distinction between a significant difference and an important difference is:
A) The level of significance used (.05 or .01)
B) Possible violations of the assumptions of homogeneity of variance and normality
C) The number of cases in each group
D) The nature of the alternative hypothesis
C) The number of cases in each group
Violation of the assumption of homogeneity of variance has less detrimental effect when:
A) n₁ and n₂ are of equal size
B) n₁ and n₂ are both large
C) Either (A) or (B) is true
D) The sampling distribution is non-normal
C) Either (A) or (B) is true
Combining data from two samples to make a pooled variance estimate is logically justified when:
A) It can be assumed that the two population standard deviations are equal
B) The two sample standard deviations are unequal
C) The two ns are equal
D) The two samples are dependent
A) It can be assumed that the two population standard deviations are equal
The assumption of homogeneity of variance means that:
A) The scores in the two populations show little variability
B) The scores in the two populations are equally variable
c) the scores in the two samples show little variability
d) the scores in the two samples are equally variable
B) The scores in the two populations are equally variable
In order for critical values of t to be precisely correct for testing H₀: µ₁ - µ₂ = 0 using small independent samples, we must assume: A) σ₁ = σ₂ B) Normality of populations C) µ₁ = µ₂ D) All of the above
D) All of the above
In order for critical values of t to be precisely correct for testing H₀: µ₁ - µ₂ = 0 using small independent samples, we do not need to assume: A) σ₁ = σ₂ B) n₁ = n₂ C) µ₁ = µ₂ D) All of the above
B) n₁ = n₂
The symbol d represents: A) The effect size, estimated from sample data B) The difference, x̄₁ - x̄₂ C) The discrepancy between σ₁ and σ₂ D) The discrepancy between n₁ and n₂
A) The effect size, estimated from sample data
You conduct an experiment with two groups and find a statistically significant difference between the two sample means. Which of the following conditions would undermine your confidence in concluding that the treatment condition caused this difference?
A) n₁ ≠ n₂
B) σ₁ ≠ σ₂
C) α = 0.15
D) Subjects were not randomly assigned to two groups
D) Subjects were not randomly assigned to two groups
Given x̄₁ = 80, n₁ = 25, x̄₂ = 65, n₂ = 27, s(pooled) = 7.5, ES equals: A) 15 B) 50 C) 2.0 D) None of the above
C) 2.0
When using a t test to analyze the results of an experiment using college sophomore volunteers, the assumption of random sampling:
A) Is fulfilled if a random procedure is used to assign subjects to treatment groups
B) Places strict limits on all generalizations
C) Places strict limits on statistical generalizations
D) All of the above
C) Places strict limits on statistical generalizations
As used in most social science experiments, statistical inference procedures do not provide us with:
A) The authority to make inferences beyond our particular set of conditions and type of subjects
B) A means of accounting for chance sampling variation in our particular sample results
C) A means of determining the kinds of results that would be expected as a result of chance factors
D) All of the above
A) The authority to make inferences beyond our particular set of conditions and type of subjects
The basic assumption underlying all the inference techniques described in this text is: A) Normality B) Randomization C) Random sampling D) Homogeneity of variance
C) Random sampling
Thirty out of 60 subjects are randomly assigned to the experimental group and the remaining 30 to the control group. This procedure is technically known as: A) Random sampling B) Experimental control C) Unbiased assignment D) None of the above
D) None of the above
