Chapter 9 One-Sample & Two- Sample Independent Sample t Tests

Two researchers (A and B) compute a one-sample t test. For both tests, the mean difference between the sample and value stated in the null hypothesis is 5, but the standard error is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?

Researcher A.

The mean crying time of infants during naptime at a local preschool is 12 minutes. The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8 ± 4.6 (M ± SD) minutes. Test whether this new naptime routine reduced crying time at a 0.05 level of significance.

The new naptime routine significantly reduced crying time, t(24) = −4.35, p < 0.05.

A researcher records the number of distracters (such as noises) that preschool-aged children ignore while watching a popular Sunday morning cartoon show. Assuming that the population variance is unknown, what type of t test is appropriate for this study?

one-sample t test

The ______ is an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis.

t statistic

A researcher reports that the mean difference in response time to an auditory versus a visual cue is 0.83 seconds, with a pooled sample variance equal to 2.45. What is the effect size for this test using estimated Cohen's d?

d = 0.53; medium effect size

A researcher conducts two t tests. Test 1 is a two-tailed test with a smaller sample size at a 0.05 level of significance. Test 2 is a two-tailed test with a larger sample size at a 0.05 level of significance. What do you know about the degrees of freedom for each test?

Test 2 is associated with larger degrees of freedom.

A researcher conducts two t tests. Test 1 is a one-tailed test with a smaller sample size at a .05 level of significance. Test 2 is a one-tailed test with a larger sample size at a .05 level of significance. What do you know about the critical values for each test?

Test 2 is associated with smaller critical values.

Which of the following is an assumption for computing any type of independent sample t test?

> Data in the population being sampled are normally distributed. > Data were obtained from a sample that was selected using a random sampling procedure. > The probabilities of each measured outcome in a study are independent. > all of the above

The estimated standard error in the t statistic uses the ______ to estimate the ______ when the population variance is unknown.

> sample variance > population variance

How does our estimate of the population variance change as the sample size increases? Explain.

As sample size increases, the sample variance more closely estimates the population variance.

Which measure of effect size is most commonly reported with a t test?

Cohen's d

A t distribution with infinite degrees of freedom is a z distribution.

True

A key difference between a t statistic and a z statistic is that the standard error is ______ to compute a t statistic.

estimated

What measure of effect size is most often reported with the t-test?

estimated Cohen's d

In the following studies, state whether you would use a one-independent or two-independent sample t-test. (a) a study testing whether night-shift workers sleep the recommended 8 hours per day

one-independent sample t-test

In the following studies, state whether you would use a one-independent or two-independent sample t-test. (b) a study measuring differences in attitudes about morality among Democrats and Republicans

two-independent sample t-test

In the following studies, state whether you would use a one-independent or two-independent sample t-test. (c) an experiment measuring differences in brain activity among rats placed on either a continuous or intermittent reward schedule

two-independent sample t-test

State the critical value(s) for the following two-tailed t test at a .05 level of significance: t(∞).

±1.96 and the same as for a two-tailed z test at a .05 level of significance

You read about a study testing whether night shift workers sleep the recommended 8 hr/day. Assuming that the population variance of sleep (per day) is unknown, what type of t test is appropriate for this study?

one-sample t test

Will each of the following increase, decrease, or have no effect on the value of the test statistic in a one-independent sample t-test? (d) The difference between the sample and population mean increased.

This change will increase the value of the test statistic.

A researcher reports a significant mean difference in a given population. If she computes both eta-squared and omega-squared to measure the effect size, then which estimate will be the most conservative?

omega-squared

Which of the following summarizes a t test that was significant and associated with a large effect size?

t(12) = 2.95, p < .05, d = .82

Will each of the following increase, decrease, or have no effect on the value of the test statistic in a one-independent sample t-test? (b) The sample variance is doubled.

This change will decrease the value of the test statistic.

Will each of the following increase, decrease, or have no effect on the value of the test statistic in a one-independent sample t-test? (c) The level of significance is reduced from 0.05 to 0.01.

This change will have no effect on the value of the test statistic.

Will each of the following increase, decrease, or have no effect on the value of the test statistic in a one-independent sample t-test? (a) The sample size is increased.

This change will increase the value of the test statistic.