Module 6 Knowledge Check

Which bit of information is not obtainable from the results of a t-test written up in a statistical report?

Each of these bits of information is obtainable from the results of a t-test written up in a statistical report.

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?

It is flatter and more spread out than the normal distribution.

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

Larger sample variance increases the estimated standard error but decreases measures of effect size.

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?

The sample with the smaller variance will produce the larger t statistic.

Consider a sample with M = 16 and s2 = 25. A researcher is testing the null hypothesis that µ = 20. Which statement is correct?

The treatment has a large effect size (Cohen's d).

A sample has a mean of M = 39.50, a standard deviation of s = 4.30, and produces a t statistic of t = +2.14. For a two-tailed hypothesis test, which of the following is the correct statistical decision for this sample?

This is impossible to determine based on the provided information.

A researcher selects a sample from a population with µ = 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?

an increased sample size

A researcher conducts a hypothesis test using a sample of n = 20 with M = 34 and s2 = 36 from an unknown population. What is the df value for the t statistic?

df = 19

If n = 63 for a two-tailed hypothesis test in which a t-test should be utilized, which df value should be referenced when using the abridged t distribution table in the textbook in order to set the critical t values for the hypothesis test?

df = 60

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

if the sample size is large and the sample variance is small

If other factors are held constant, which set of sample characteristics is most likely to produce a statistically significant t statistic?

n = 100 with s2 = 100

The results of a hypothesis test are reported as follows in a scientific report: t(15) = 2.70, p < .05. Based on this report, how many individuals were in the sample?

n = 16

Which of the following samples will have the smallest value for the estimated standard error?

n = 16 with s2 = 16

A sample with a mean of M = 40 and a variance of s2 = 12 has an estimated standard error of 2 points. How many scores are in the sample?

n = 3

A researcher conducts a hypothesis test using a sample from an unknown population. If df = 30 for the t statistic and M = 46 and s2 = 10, how many individuals were in the sample?

n = 31

A sample of n = 4 scores has SS = 60. Which is the variance for this sample?

s2 = 20

A sample of n = 7 scores has a mean of M = 65 and an estimated standard error of 2 points. What is the sample variance?

s2 = 28

What is the sample variance and estimated standard error for a sample of n = 9 scores with SS = 72?

s2 = 9 and sM = 1

A sample of n = 25 scores has a mean of M = 40 and a standard deviation of s = 10. What is the estimated standard error for the sample mean?

sM = 2

If a treatment produces a sample mean of M = 25 with s = 18 among a sample of n = 36, which t-statistic should be obtained and which decision should be made if conducting a two-tailed hypothesis test with α = .05 and an expected mean of µ= 30?

t = -1.67 and fail to reject H0

It is expected that a treatment will reduce scores on a variable. If α = .05, what is the critical t value for a one-tailed hypothesis test with n = 15?

t = -1.761

On average, which value is expected for the t statistic when the null hypothesis is true?

t = 0.00

If a sample of n = 22 scores is being used to make an 90% confidence interval estimate of the population mean (µ), which values of t should be used?

t = ±1.721

With α = .05, the two-tailed critical region for a t test using a sample of n = 20 participants would have boundaries of _____.

t = ±2.093.

Which of the following is consistent with what r2 represents as a measure of effect size?

the portion of variability in a sample attributable to a treatment effect relative to the total variability in the sample

Which of the following is not needed to compute a t statistic?

the value of the population variance or standard deviation

If a treatment is expected to increase scores on a variable for which the mean is expected to be µ = 100, what is the null hypothesis?

µwith treatment < 100