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Exam 9: Introduction to the T Statistic

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Question 31

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A sample of n = 25 scores produces a t statistic of t = 2.062.If the researcher is using a two-tailed test,which of the following is the correct statistical decision?

A) The researcher can reject the null hypothesis with α = .05 but not with α = .01.
B) The researcher can reject the null hypothesis with either α = .05 or α = .01.
C) The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.
D) It is impossible to make a decision about H₀ without more information.

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Question 32

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For a two-tailed test with α = .05 and a sample of n = 16,the boundaries for the critical region are t = ±2.120.

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Question 33

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Why are t statistics more variable than z-scores?

If other factors are held constant,as the sample variance increases,the estimated standard error also increases.

Two samples from the same population both have n = 10 scores with M = 45.If the t statistic is computed for each sample,then what is the relationship between the two t values?

If two samples,each with n = 20 scores,are selected from the same population and both have the same mean (M = 53)and the same variance (s² = 12),then they will also have the same t statistic.

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.

A researcher is using a two-tailed hypothesis test with α = .05 to evaluate the effect of a treatment.If the boundaries for the critical region are t = ± 2.080,then how many individuals are in the sample?

How does sample variance influence the estimated standard error and measures of effect size such as r² and Cohen's d?

If a sample of n = 16 scores is being used to make an 80% confidence interval estimate of the population mean,μ,what value(s) of t should be used?

A random sample with n = 20 scores has df = 19.

A research report states "t(8)= 2.00,p > .05." For this test,r² = 2/10.

A sample of n = 4 scores is selected from a population with an unknown mean.The sample has a mean of M = 40 and a variance of s² = 16.Which of the following is the correct 90% confidence interval for μ?

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

Which of the following would have no effect on the width of a confidence interval?

Under what circumstances can a very small treatment effect be statistically significant?

If a hypothesis test using a sample of n = 16 scores produces a t statistic of t = 2.15,then the correct decision is to reject the null hypothesis for a two-tailed test with  = .05.

If two samples from the same population are the same size and have the same mean,then they will have the same t statistic.

A sample with a mean of M = 40 and a variance of s² = 20 has an estimated standard error of 1 point.How many scores are in the sample?

The sample mean will always be exactly in the center of a confidence interval that is estimating the value of the population mean.