PSYCH 104 - Ch 9 TEST - Means One-Sample and Two-Independent-Sample t Tests

What are the degrees of freedom for each of the following samples? a) n = 12 b) n = 22 c) n = 5 d) n = 30

(a) df = 11, (b) df = 21, (c) df = 4, (d) df = 29

Assuming α = .05, what is the critical value in each of the following t distributions? df = 10, two-tailed test df = 30, one-tailed test (lower tail critical) df = ∞, two-tailed test df = 15, one-tailed test (upper tail critical)

(a) ± 2.228, (b) − 1.697, (c) ± 1.96, (d) 1.753

A researcher computes the following test statistic for a two-independent sample t-test: t(28) = 2.97, p < .05. What is the proportion of variance for this test using the formula for eta-squared?

0.24

A researcher conducts a one-independent sample t-test. What are the critical values for a two-tailed hypothesis test at a .05 level of significance when df = 14?

2.145

A researcher conducts a two-independent sample t-test with a sample of 24 participants, where 12 participants are observed in each group. What are the degrees of freedom for this hypothesis test?

22

How does increasing sample size affect the estimate of the population variance?

As sample size increases, the sample variance more closely approximates the population variance

What is the main limitation of the z test in behavioral research?

It requires that the population variance is known, and behavioral researchers rarely know the value of the population variance

What are three assumptions of the one-sample t test?

Normality, random sampling, and independence

What are the four assumptions for the two-independent-sample t test?

Normality, random sampling, independence, and (equal) homogeneity of variances

What measure, eta-squared or omega-squared, gives a more conservative or smaller estimate of proportion of variance?

Omega-squared

An estimated Cohen's d substitutes which value in the formula to estimate the population standard deviation?

Sample standard deviation

What value is placed in the denominator for the two-independent-sample t test?

The estimated standard error for the difference

What is the denominator for computing an estimated Cohen's d for a two-independent-sample t test?

The pooled sample standard deviation

The t-statistic is an inferential statistic used to determine the number of standard deviations in a t-distribution that a sample mean deviates from:

a population mean or mean difference stated in the null hypothesis

If the difference between two means is 4, then what will the estimated Cohen's d value be with a pooled sample standard deviation of each of the following? a) 4 b) 8 c) 16 d) 40

a) 4/4=1.00 b) 4/8=0.50 c) 4/16=0.25 d) 4/40=0.10

A researcher compares the mean grade point average (GPA) of college students with a full-time job to the mean GPA of the general population of college students. In this example, identify (a) the dependent variable and (b) the treatment.

a) GPA b) Having a full-time job

State whether each of the following values for estimated Cohen's d has a small, medium, or large effect size. a) 0.40 b) 1.20 c) 0.05 d) 0.10

a) Medium b) Large c) Small d) Small

Using the same example as in Question 3, what is the researcher's decision if she reports the following values for the test statistic? a) 2.558 b) 1.602 c) 2.042 d) −2.500

a) Reject the null hypothesis, b) Retain the null hypothesis, c) Retain the null hypothesis, d) Reject the null hypothesis

Using the same study described in Question 2 with α = .01, what is the decision if the following values for the test statistic are obtained? a) 2.558 b) 1.602 c) 2.999 d) 3.404

a) Retain the null hypothesis b) Retain the null hypothesis c) Reject the null hypothesis d) Reject the null hypothesis

Why does the t-distribution have greater variability in the tails of the distribution compared to a normal distribution?

because the sample variance is substituted for the population variance to estimate the standard error in this distribution

The two-independent sample t-test can be only computed when:

different participants are observed one time in each group

What is the calculation for the degrees of freedom of a t distribution?

n − 1

A researcher computes the following test statistic for a one-independent sample t test, t(16) = 2.900, p < .05. What is the proportion of variance for this test using the formula for omega-squared?

not enough information

What value is placed in the denominator of the formula for estimated Cohen's d for the two-independent sample t-test?

pooled sample standard deviation

Suppose a researcher observes 16 participants assigned to an experimental group (n = 16) and 16 assigned to a control group (n = 16). Scores in the experimental group were 32 ± 8 (M ± SD); scores in the control group were 32 ± 12 (M ± SD). If the null hypothesis is that the mean difference equals 0, then what is the decision for a two-independent sample t-test at a .05 level of significance?

retain the null hypothesis

What value is placed in the denominator of the formula for estimated Cohen's d for the one-independent sample t test?

sample standard deviation

The __________________ is a normal-like distribution with greater variability in the tails than a normal distribution because the sample variance is substituted for the population variance to estimate the standard error in this distribution.

t distribution

To report the results of a t-test, which of the following is not reported?

the critical value

A researcher compares the mean difference between two groups with 15 students in each group and reports the following result for a two-independent sample t-test: t(29) = 3.52, p < .05. If this is a two-tailed test at a .05 level of significance, then what must be incorrect with this result?

the degrees of freedom

The one-independent sample t-test can be computed only when:

the population being sampled from is normally distributed

A sample of 25 mothers rated how important they thought patience was for being a good mother. Women reported an average rating of 1.1 ± 1.0 (M ± SD) on a rating scale from -3 (not important at all) to +3 (very important). If the null hypothesis is that the rating equals 0, then test whether or not women find patience important at a .05 level of significance (two-tailed test).

women rated patience as being significantly important, t(24) = 5.50, p < .05

A researcher reports the following result for a t-test at a .05 level of significance: t(40) = 3.02, p < .05 (d = .22). Is this result significant?

yes, for both a one- or a two-independent sample t-test

A researcher measures the time it takes 13 men and 15 women to complete multiple tasks in a study. She compares the mean difference between men and women using the two-independent-sample t test. What is the critical value for this test if she conducts a two-tailed test at a .05 level of significance?

± 2.056

Researchers record the number of errors on some behavioral task for 15 participants. They report a sample mean equal to 6 ± 1 (M ± SD). What is the critical value for a two-tailed test with α = .01?

± 2.977

The value of the test statistic for a two-independent-sample t test is 2.400. Using eta-squared, what is the proportion of variance when the degrees of freedom are 30?

η2 = (2.4)^2/(2.4)^2+30 = 0. 16 ( medium effect )

A researcher reports that a sample of workers with high-stress careers slept significantly less than workers in the general population, t( 48) = 2.36, p < .05. Compute eta-squared for this one-sample t test.

η2 = .10

Using the same example as in Question 3, what is the proportion of variance using omega-squared?

ω2 = (2.4)^2 − 1/(2.4)^2 + 30 = 0.13 ( medium effect )