Stats Exam 2 Quizzes
If the null hypothesis is true, what value is expected, on average, for the repeated-measures t statistic? 1 0 1.96 t > 1.96
0
The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 16.If there are n = 8 scores in each sample, then what is the estimated standard error for the sample mean difference? 2 4 128 16
2
A researcher reports t(22) = 5.30, p < .01 for an independent-measures experiment. How many individuals participated in the entire experiment? 21 23 20 24
24 (n-2)
If n = 15 for each sample, which of the following sets of data provides the clearest difference between the two samples? : A sample mean difference of 10 points with s2 = 10 for both samples : A sample mean difference of 5 points with s2 = 5 for both samples : A sample mean difference of 10 points with s2 = 5 for both samples : A sample mean difference of 5 points with s2 = 10 for both samples
: A sample mean difference of 10 points with s2 = 5 for both samples
For the independent-measures t statistic, what is the effect of increasing the sample variances? : Decrease the likelihood of rejecting H0 and increase measures of effect size. : Increase the likelihood of rejecting H0 and increase measures of effect size. : Decrease the likelihood of rejecting H0 and decrease measures of effect size. : Increase the likelihood of rejecting H0 and decrease measures of effect size.
: Decrease the likelihood of rejecting H0 and decrease measures of effect size.
For a normal distribution, proportions in the right-hand tail are positive and proportions in the left-hand tail are negative. : True : False
: False
For a normal distribution, the proportion located between z = -1.00 and z = +1.00 is p = 34.13%. : True : False
: False
If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic? : The two samples both have n = 15 with variances of 120 and 125. : The two samples both have n = 30 with variances of 120 and 125. : The two samples both have n = 15 with sample variances of 20 and 25. : The two samples both have n = 30 with sample variances of 20 and 25.
: The two samples both have n = 30 with sample variances of 20 and 25.
A repeated-measures design has the maximum advantage over an independent-measures design when ____. : very few subjects are available and individual differences are small : many subjects are available and individual differences are small : many subjects are available and individual differences are large : very few subjects are available and individual differences are large
: very few subjects are available and individual differences are large
A matched-subjects study and an independent-measures study both produced a t statistic with df = 16. How many individuals participated in each study? : 17 for matched-subjects and 18 for independent-measures : 18 for matched-subjects and 18 for independent-measures : 17 for matched-subjects and 17 for independent-measures : 34 for matched-subjects and 18 for independent-measures
: 34 for matched-subjects and 18 for independent-measures
Which of the following sets of data would produce the largest value for an independent-measures t statistic? : The two sample means are 10 and 20 with variances of 20 and 25 : The two sample means are 10 and 12 with sample variances of 20 and 25 :The two sample means are 10 and 20 with variances of 120 and 125 :The two sample means are 10 and 12 with variances of 120 and 125
: The two sample means are 10 and 20 with variances of 20 and 25
For which of the following situations would a repeated-measures research design be appropriate? : comparing mathematical skills for girls versus boys at age 10 : comparing pain tolerance with and without acupuncture needles : comparing self-esteem for students who participate in school athletics versus those who do not : comparing verbal solving skills for science majors versus art majors at a college
: comparing pain tolerance with and without acupuncture needles
For any normal distribution, exactly 97.50% of the z-score values are less than z = 1.96. True False
:TRUE
A sample of n = 16 individuals is selected from a population with μ = 60 and σ = 6 and a treatment is administered to the sample. After treatment, the sample mean is M = 63. What is the value of Cohen's d for this sample? a) 0.50 b) 3.00 c) 0.33 d) 2.00
A) 0.50
What term is used to identify the standard deviation of the distribution of sample means? A) the expected value of M B) the standard error of M C) the sample mean D) the central limit mean
B) the standard error of M
What proportion of a normal distribution is located between the mean and z = 1.40? A) 0.9192 B) 0.0808 C) 0.4192 D) 0.8384
C) 0.4192
A sample of n = 16 scores is selected from a population with μ = 100 and σ = 32. If the sample mean is M = 104, what is the z-score for this sample mean? A) 2.00 B) 1.00 C) 0.50 D) 0.25
C) 0.50
A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 76? A) 0.1915 B) 0.3085 C) 0.6915 D) 0.3830
C) 0.6915
If all the possible random samples with n = 36 scores are selected from a normal population with µ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average of all the sample means? A) 2 B) 6 C) 80 D) It cannot be determined without additional information.
C) 80
If a sample of n = 4 scores is obtained from a population with μ = 70 and σ = 12, then what is the z-score corresponding to a sample mean of M = 76? A) z = 0.25 B) z = 0.50 C) z = 1.00 D) z = 2.00
C) Z = 1.00
A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18. If the sample mean is M = 76, then what is the z-score for the sample mean? A) z = 0.33 B) z = 0.50 C) z = 1.00 D) z = 3.00
C) z = 1.00
If a treatment has a very small effect, then what is a likely outcome for a hypothesis test evaluating the treatment? a) Correctly reject the null hypothesis b) A Type I error c) Correctly fail to reject the null hypothesis d) A Type II error
D) A Type II error
A sample is obtained from a population with μ = 100 and σ = 20. Which of the following samples would produce the most extreme z-score? A) A sample of n = 25 scores with M = 102 B) A sample of n = 100 scores with M = 102 C) A sample of n = 25 scores with M = 104 D) A sample of n = 100 scores with M = 104
D) A sample of n = 100 scores with M = 104
Under what circumstances is distribution of sample means normal? A) It is always normal B) Only if the population distribution is normal C) If the sample size is greater than 30 D) If the population is normal or if the sample size is greater than 30
D) If the population is normal or if the sample size is greater than 30
One sample of n = 8 scores has a variance of s2 = 6 and a second sample of n = 8 scores has s2 = 10.If the pooled variance is computed for these two samples, then the value obtained will be ____. closer to 6 than to 10 closer to 10 than to 6 equal to 10 exactly half way between 6 and 10
Exactly half way between 6 and 10
A sample is obtained from a population with s = 20. If the sample mean has a standard error of 5 points, then the sample size is n = 4. True False
FALSE
A sample of n = 4 scores is selected from a population with µ = 30 and s = 8. The probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 2.00 from a normal distribution. True False
FALSE
A sample of n = 9 scores is randomly selected from a population with µ = 80 and s = 9. If the sample mean is M = 83, then the corresponding z-score is z = +3.00. True False
FALSE
A vertical line is drawn through a normal distribution dividing the distribution into two parts. If the smaller part equals 0.1915 of the distribution, then the line was drawn at z = 0.50 or at z = -0.50. True False
FALSE
As the sample size increases, the standard error also increases. True False
FALSE
Even if a treatment has an effect, it is still possible to obtain a sample mean that is very similar to the original population mean. What outcome is likely if this happens? a) Reject H0 and make a Type I error. b) Fail to reject H0 and make a Type II error. c) Correctly fail to reject H0. d) Correctly reject H0.
Fail to reject Ho and make a Type ll error
A repeated-measures study and an independent-measures study both produce a t statistic with df = 20. The repeated-measures study used more subjects than the independent-measures study. True False
False
If a hypothesis test leads to rejecting the null hypothesis, it means that the data did not provide enough evidence to conclude that the treatment has an effect. a) True b) False
False
In a hypothesis test, a large value for the sample variance increases the likelihood that you will find a significant treatment effect. True False
False
In a repeated measures study, the null hypothesis says that the mean for the sample of difference scores should be equal to zero. True False
False
The null hypothesis for the independent-measures t test states that there is no difference between the two sample means. True False
False
When pooling variances, the resulting value will be closer to the variance for the sample with the smaller number of scores. True False
False
If one sample has n = 5 scores with SS = 40 and a second sample has n = 5 scores with SS = 20, then the pooled variance will be 60/10 = 6. True False
False
Compared to an independent-measures design, a repeated-measured study is more likely to find a significant effect because it reduces the contribution of variance due to ____. individual differences degrees of freedom the effect of the treatment MD
Individual differences
In general, if the variance of the difference scores increases, then what will happen to the value of the t statistic? : It may increase or may decrease. There is no consistent relationship between variance and the size of the t statistic. : It will increase (move farther toward the tail of the distribution). : It will decrease (move toward 0 at the center of the distribution). : It will stay the same; the t statistic is not affected by the variance of the difference scores.
It will decrease
Which combination of factors is most likely to produce a significant value for an independent-measures t statistic? small samples and small variance large samples and large variance large samples and small variance small samples and large variance
Large samples and small varience
A sample of n = 25 scores is selected from a population with a mean of µ = 80 and a standard deviation of σ = 20. The expected value for the sample mean (that is, the mean of the sampling distribution of means) is 80. True False
TRUE
If samples of size n = 16 are selected from a population with μ = 40 and σ = 8, the distribution of sample means will have an expected value (mean) of 40. True False
TRUE
The law of large numbers states that the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean.. True False
TRUE
In an independent-measures hypothesis test, what must be true if t = 0? The two sample means are not equal. The two sample variances must be equal. The two population means must be equal. The two sample means must be equal.
The two sample means must be equal
A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment. If all of the participants show improved performance of 8 or 9 points after treatment, then the researcher should find ____. : the variance of the difference scores is near zero : a very large variance in the difference scores : a sample mean difference near zero : a t statistic near zero
The variance of the difference scores is near zero
A Type I error occurs when a researcher concludes that a treatment has an effect but, in fact, the treatment has no effect. :True :False
True
A Wilcoxon test can be used if there is reason to suspect that one of the assumptions for the repeated-measures t test has been violated. True False
True
A research report states "t(15) = 2.31, p < .05." For this study, the sample had n = 16 scores. True False
True
As sample size increases, the critical region boundaries for a two-tailed test with a = .05 will move closer to zero. a) True b) False
True
Compared to a z-score, a hypothesis test with a t statistic requires more information (evidence) from the sample to be significant. True False
True
For a repeated-measures study, a small variance for the difference scores indicates that the treatment effect is consistent across participants. True False
True
If a research report includes the term significant result, it means that the null hypothesis was rejected. :True :False
True
If other factors are held constant, the bigger the sample is, the greater the likelihood of rejecting the null hypothesis. a) True b) False
True
If other factors such as sample size, alpha level, and population standard deviation are held constant, the larger the size of the treatment effect, the greater the power of the hypothesis test. a) True b) False
True
If random samples, each with n = 20 scores, are selected from a population, and the z-score and t statistic are computed for each sample, the t statistics will be more variable than the z-scores. True False
True
The independent-measures t statistic uses the data from two separate samples to draw inferences about the mean difference between two populations or between two different treatment conditions. True False
True
The power of a hypothesis test is the probability that the sample mean will be in the critical region if the treatment has an effect. :True :False
True
The value obtained for Cohen's d is independent of the sample size. a) True b) False
True
Two samples are selected from a population and a treatment is administered to the samples. If both samples have the same mean and the same variance, you are more likely to find a significant treatment effect with a sample of n = 100 than with a sample of n = 4. True False
True
Two samples from same population probably will have different t statistics even if they are the same size and have the same mean. True False
True
Which set of characteristics will produce the smallest value for the estimated standard error? a) A small sample size and a large sample variance b) A large sample size and a small sample variance c) A large sample size and a large sample variance d) A small sample size and a small sample variance
b) A large sample size and a small sample variance
A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? a) A sample mean near 80 for a large sample b) A sample mean much different than 80 for a large sample c) A sample mean near 80 for a small sample d) A sample mean much different than 80 for a small sample
b) A sample mean much different than 80 for a large sample
With α = .05 and df = 8, the critical values for a two-tailed t test are t = ±2.306. Assuming all other factors are held constant, if the df value were increased to df = 20, what would happen to the critical values for t? a) There is not enough information to answer. b) They would decrease (move closer to zero). c) They would stay the same. d) They would increase (move farther from zero)
b) They would decrease (move closer to zero).
A normal distribution has a mean of µ = 40 with σ = 10. What proportion of the scores in this distribution are greater than X = 55? a) 0.3085 b) 0.6915 c) 0.0668 d) 0.9332
c) 0.0668
A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 80 and X = 100? a) 0.8413 b) 0.1587 c) 0.3413 d) 0.6826
c) 0.3413
What is the consequence of a Type II error? a) Concluding that a treatment has an effect when it really does b) Concluding that a treatment has an effect when it really has no effect c) Concluding that a treatment has no effect when it really does d) Concluding that a treatment has no effect when it really has no effect
c) Concluding that a treatment has no effect when it really does
John drives to work each morning and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John's drive to work will take less than 35 minutes? a) 0.6554 b) 0.3446 c) 0.7257 d) 0.2743
d) 0.2743
What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72? a)s2 = 9 and sM = 3 b) s2 = 3 and sM = 1 c) s2 = 3 and sM = 3 d) s2 = 9 and sM = 1
d) s2 = 9 and sM = 1
Which of the following describes the function of a confidence interval? a) It uses a level of confidence to estimate a sample mean. b) It uses a population mean to predict a sample mean. c) It uses the sample mean to determine a level of confidence. d) It uses a sample mean to estimate the corresponding population mean.
d) It uses a sample mean to estimate the corresponding population mean.
What z-score values form the boundaries for the middle 60% of a normal distribution? a) z = +0.25 and z = -0.25 b) z = +0.39 and z = -0.39 c) z = +0.52 and z = -0.52 d) z = +0.84 and z = -0.84
d) z = +0.84 and z = -0.84
A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 35, how many individuals were in the sample? n = 34 n=32 n = 35 n = 36
n = 36
For the repeated-measures t statistic, where n1 and n2 are the number of scores before and after treatment, and n = n1= n2, df = ____. n1 + n2 - 1 n - 1 n1 + n2 - 2 n - 2
n-1
A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 6. What is the probability that the sample mean will be greater than M = 43? A) 0.3085 B) 0.6915 C) 0.9332 D) 0.0668
D) 0.0668