Exam 3 Study Guide

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Feb 20, 2024

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A matched-subjects study and an independent-measures study both produced a t statistic with df = 10. How many individuals participated in each study? 22 for matched-subjects and 12 for independent-measures A random sample with n = 20 scores has df = 19. True 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. False A repeated-measures study comparing two treatments with n = 4 participants produces MD = 2 and SS = 75 for the difference scores. What is the estimated standard error for the sample mean difference? 2.5 A repeated-measures test usually is more likely to detect a real treatment effect than an independent-measures test because the repeated-measures design typically has a smaller variance and a smaller estimated standard error. True A research report describing the results from a repeated-measures study states that the data show no significant difference between the two treatments, t(10) = 1.65, p > .05. Based on this report, how many individuals participated in the research study? 11 A research report describing the results from a repeated-measures t test states that "t(22) = 1.71, p > .05." From this report, what was the outcome of the hypothesis test? Fail to reject the null hypothesis with a sample of n = 23 participants A research study produces a t statistic with df = 14. For this study, which of the following designs would require a total of 30 participants? A matched-subjects design A researcher predicts that scores in treatment A will be higher than scores in treatment B. If the mean for the 10 participants in treatment A is 4 points higher than the mean for the 10 participants in treatment B and the data produce t = 2.095, what decision should be made? With α = .05, reject H0 for a one-tailed test but fail to reject for a two-tailed test A researcher reports an independent-measures t statistic with df = 30. If the two samples are the same size (n1 = n2), then how many individuals are in each sample? 16 A researcher reports df = 18 for a repeated-measures t statistic. This research study used a total of n = 19 participants. True A researcher reports t(12) = 2.86, p < .05 for a repeated-measures research study. How many individuals participated in the study? n=13 A researcher reports t(22) = 5.30, p < .01 for an independent-measures experiment. How many individuals participated in the entire experiment? 24 A researcher selects a sample from a population with = 30 and uses the sample to evaluate the effect of a treatment. After treatment, the sample has a mean of M = 32 and a variance of s2 = 6. If Cohen's d is used to measure the size of the treatment effect, which of the following would have no effect on the value of Cohen's d? Increase the number of individuals in the sample A researcher selects a sample from a population with a mean of = 40 and administers a treatment to the individuals in the sample. If the treatment is expected to decrease scores, which of the following is the correct statement of the null hypothesis for a one-tailed test? μ= > 40 A researcher selects a sample from a population with a mean of μ = 40 and administers a treatment to the individuals in the sample. If the treatment is expected to decrease scores, which of the following is the correct statement of the null hypothesis for a one-tailed test? μ = or >40

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, what should the researcher find? The variance of the difference scores is near zero. A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment. What would be the value of df for the repeated-measures t statistic? df=19 A sample has a mean of M = 39.5 and a standard deviation of s = 4.3, and produces a t statistic of t = 2.14. For a two-tailed hypothesis test with α = .05, what is the correct statistical decision for this sample? It is impossible to make a decision about H0 without more information. A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s 2 = 16. Based on this information, what is the value of Cohen's d ? d=0.50 A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d? d=0.50 A sample is selected from a population with μ = 70, and a treatment is administered to the sample. After treatment, the sample mean is M = 74, and Cohen's d is d = 1.00. What is the value of the sample variance? s2 = 16 A sample is selected from a population with μ = 70, and a treatment is administered to the sample. After treatment, the sample mean is M = 74, and Cohen's d is d = 1.00. What is the value of the sample variance? s2=16 A sample of n = 4 scores has SS = 60. What is the variance for this sample? 20 A sample of n = 4 scores with SS = 48 has a variance of s2 = 16 and an estimated standard error of 2. True A sample of n = 9 scores has a variance of s2 = 36. What is the estimated standard error for the sample mean? 2 Although a repeated-measures study measures two scores for each participant, the sample mean and variance are computed using only one score for each participant. True An independent-measures research study uses a total of 18 participants to compare two treatment conditions. If the results are used to construct a 90% confidence interval for the population mean difference, then the t values will be ±1.746. True An independent-measures study produces t(10) = 3.00, p < .05. For this study, if effect size is measured with r2, then r2 = 3/13. False As the sample size is increased, the distribution of t statistics becomes flatter and more spread out. False Compared to a z-score, a hypothesis test with a t statistic requires less information from the population. True Confidence intervals with the independent-measures t statistic are used to estimate how much difference there is between two population means. True For a repeated-measures study comparing two treatment conditions, a researcher obtains a sample of n = 9 difference scores with a mean of MD = 4 and a variance of s2 = 36. What is the value for the repeated-measures t statistic for these data? 4/2

For a repeated-measures study comparing two treatments with a sample of n = 9 participants, the difference scores have a mean of MD = 4.90 with SS = 72. What is the estimated standard error for the sample mean difference? 1 For a repeated-measures study, if the null hypothesis is true, then what value should be obtained for the sample mean? MD near 0 For a repeated-measures study, if the null hypothesis is true, then what value should be obtained for the sample mean? MD near 0 Next For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples? Increase the likelihood of rejecting H0 and have little or no effect on measures of effect size For an independent-measures t statistic, you typically must compute the pooled variance before calculating the estimated standard error. True If a set of n = 9 difference scores has a mean of MD = 3.5 and a variance of s2 = 36, then the standard error for the sample mean difference is 4 points. False If one sample has n = 4 and SS = 90 and a second sample has n = 8 and SS = 150, then the estimated standard error for the sample mean difference is 9 points.False If other factors are held constant, the larger the difference between the two sample means, the greater the likelihood that the independent-measures t-test will find a significant difference. True If other factors are held constant, the larger the two sample sizes, the greater the likelihood that the independent-measures t test will find a significant difference. True If other factors are held constant, the larger the values for the two sample variances, the greater the likelihood that the independent-measures t test will find a significant difference. False If other factors are held constant, which of the following sets of data is most likely to produce a significant mean difference? A sample mean difference of 10 points with n = 10 for both samples If two sample variances are not equal, the pooled variance will be closer to the larger of the two variances. False If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic? The samples are the same size and have the same mean and the same variance If two samples from the same population are the same size and have the same mean, then they will have the same t statistic. False In a hypothesis test, a large value for the sample variance increases the likelihood that you will find a significant treatment effect. False In a repeated-measures study comparing two treatments with a sample of n = 15 participants, the researcher measures two scores for each individual to obtain a total of 30 scores and the repeated-measures t statistic has df = 29. False In general, the larger the value of the sample variance, the greater the likelihood of rejecting the null hypothesis. False One concern for a repeated-measures study is that a participant's score in one treatment may be influenced by practice or experience gained in a previous treatment. True

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One sample has n = 5 scores and the second has n = 10 scores. If the pooled variance for the two samples is 30, what is the value of the estimated standard error for the sample mean difference? 3 The 95% confidence interval for the difference between two treatment means extends from 2.50 to +5.50. Based on this information, you can conclude that there is no significant difference between the treatments at the .05 level of significance. True The estimated standard error for the independent-measures t statistic provides a measure of how much difference should exist, on average, between two sample means when the null hypothesis is true. True The homogeneity of variance assumption states that the two population variances are equal. True The narrower the confidence interval, the more precise it is. With this in mind, which combination of factors will produce the most precise estimate of the difference between two population means? Two samples of n = 50 and 80% confidence The results of a hypothesis test are reported as follows: t(15) = 2.70, p < .05. Based on this report, how many individuals were in the sample? 16 The results of an independent-measures research study are reported as "t(22) = 2.12, p < .05, two tails." For this study, what t values formed the boundaries for the critical region? ±2.074 To estimate a population mean with a confidence interval, you first must estimate a range of values for t. True Two samples, each with n = 5 scores, have a pooled variance of 40. What is the estimated standard error for the sample mean difference? 4 What is the value of the estimated standard error for the following set of D-scores? Scores: 2, 2, 10, 2 2 Which combination of factors is most likely to produce a significant value for an independent- measures t statistic? Large samples and small variance Which of the following describes the effect of an increase in the variance of the difference scores in a repeated-measures design? Measures of effect size and the likelihood of rejecting the null hypothesis both decrease. Which of the following is the correct null hypothesis for a repeated-measures t test? µD = 0 Which of the following samples will have the smallest value for the estimated standard error? n = 16 with s2 = 16 Which of the following sets of data would produce the largest value for an independent-measures t statistic? Sample means of 10 and 20, with sample variances of 20 and 25. Which of the following sets of data would produce the largest value for Cohen's d ? n = 20 for both samples, a pooled variance of 15, and a mean difference of 5 points Which of the following sets of data would produce the largest value for Cohen's d? n = 20 for both samples, a pooled variance of 15, and a mean difference of 5 points Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large effect size? A large mean difference and small sample variances Why are t statistics more variable than z -scores? The extra variability is caused by variations in the sample variance.

Exam 3 Study Guide

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