Exam 9: Introduction to the T Statistic

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A hypothesis test produces a t statistic of t = 2.20.If the researcher is using a two-tailed test with α = .05,how large does the sample have to be in order to reject the null hypothesis?​

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What value is estimated with a confidence interval using the t statistic?​

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If other factors are held constant,as the sample size increases,the estimated standard error decreases.

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Two samples from same population probably will have different t statistics even if they are the same size and have the same mean.

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As the sample size is increased,the distribution of t statistics becomes flatter and more spread out.

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Compared to a z-score,a hypothesis test with a t statistic requires more information from the sample.

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If other factors are held constant,what is the effect of increasing the sample size?​

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Although you can compute a z-score for a single score (a sample of n = 1),it is impossible to compute a t statistic for a sample that has only one score.Explain why.

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If the 90% confidence interval for µ is from 40 to 50,then the sample mean is M = 45.

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If other factors are held constant,which set of sample characteristics is most likely to reject a null hypothesis stating that m = 80?​

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If the null hypothesis states that m = 70 and a researcher obtains a sample with M = 73 and s2 = 9,then Cohen's d = 0.33.

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If other factors are held constant,how does sample size influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's d?​

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A sample with a mean of M = 40 and a variance of s2 = 20 has an estimated standard error of 2 points.How many scores are in the sample?​

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For a hypothesis test using a t statistic,the boundaries for the critical region will change if the sample size is changed.

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If other factors are held constant,the bigger the sample is,the greater the likelihood of rejecting the null hypothesis.

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A sample of n = 25 scores has a mean of M = 40 and a variance of s2 = 100.What is the estimated standard error for the sample mean??

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For a one tailed test evaluating a treatment that is supposed to decrease scores,a researcher obtains t(8)= 1.90.For α = .05,the correct decision is to reject the null hypothesis.

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A sample of n = 4 scores has SS = 48.What is the estimated standard error for the sample mean?​

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A researcher is testing the effect of a new cold and flu medication on mental alertness.A sample of n = 9 college students is obtained and each student is given the normal dose of the medicine.Thirty minutes later,each student's performance is measured on a video game that requires careful attention and quick decision making.The scores for the nine students are as follows: 6,8,10,6,7,13,5,5,3. a. Assuming that scores for students in the regular population average μ = 10, are the data sufficient to conclude that the medication has a significant effect on mental performance? Test at the .05 level of significance. b. Compute r2, the percentage of variance explained by the treatment effect. c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would be presented in a research report.

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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?​

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