Question 1

With α = .05 and df = 8, the critical values for a two-tailed t test are t = ±2.306.Assuming all other factors are held constant, if the df value were increased to df = 20, what would happen to the critical values for t?

Accepted Answer

As the degrees of freedom (df) increase, the critical values for a t-distribution move closer to zero, reflecting a distribution that more closely resembles the normal distribution.

Question 2

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

Accepted Answer

A very small treatment effect can be statistically significant if the sample size is large and the sample variance is small, as this increases the power of the statistical test to detect even small effects.

Question 3

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?

Accepted Answer

The answer of A sample of n = 4 scores...

Question 4

With α = .05, what is the critical t value for a one-tailed test with n = 15?

Accepted Answer

The answer of With α = .05, what is the...

Question 5

A sample is selected from a population with μ = 46 and a treatment is administered to the sample.After treatment, the sample mean is M = 48 with a sample variance of s² = 16.Based on this information, the size of the treatment effect, as measured by Cohen's d, is ____.

Accepted Answer

Cohen's d is calculated as the difference between the sample mean and the population mean divided by the standard deviation. Here, d = (48 - 46) / 4 = 0.50.

Question 6

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?

Accepted Answer

A larger sample size increases the power of the test, which means it increases the likelihood of rejecting the null hypothesis. However, the measures of effect size such as r² and Cohen's d are not affected by sample size as they are standardized measures that are independent of the sample size. Thus, the correct answer is B that the larger sample size increases the likelihood but has little influence on measures of effect size.

Question 7

Which of the following describes what a confidence interval does?

Accepted Answer

A confidence interval uses a sample mean to estimate the corresponding population mean with a certain level of confidence. It is a range of values that is likely to contain the population parameter of interest.

Question 8

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?

Accepted Answer

The t statistic is inversely related to the sample variance; thus, the sample with the smaller variance will produce the larger t statistic.

Question 9

A hypothesis test with a sample of n = 25 participants produces a t statistic of t = +2.53.Assuming a one-tailed test with the critical region in the right-hand tail, what is the correct decision?

Accepted Answer

The answer of A hypothesis test with a sample of...

Question 10

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

Accepted Answer

A t statistic requires not only the sample mean and standard deviation, but also the sample size and the population standard deviation (or an estimate of it). In contrast, a z-score only requires the sample mean and standard deviation, as long as the sample size is sufficiently large or the population standard deviation is known.

Question 11

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?

Accepted Answer

For a two-tailed test with α = .05, the critical t-value for a sample size of n = 13 is approximately 2.179, which is less than 2.20, allowing the null hypothesis to be rejected.

Question 12

A researcher conducts a hypothesis test using a sample of n = 40 from an unknown population.What is the df value for the t statistic?

Accepted Answer

The degrees of freedom for a t-test is n-1, where n is the sample size. In this case, n = 40, so the degrees of freedom is 40-1 = 39.

Question 13

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?

Accepted Answer

The answer of A sample has a mean of M...

Question 14

When the population variance or standard deviation is not known, you must use a t statistic instead of a z?score for a hypothesis test.

Accepted Answer

When the population variance or standard deviation is not known, you must use a t statistic instead of a z-score for a hypothesis test. This is because the t-distribution takes into account the additional uncertainty introduced by estimating the population standard deviation from sample data.

Question 15

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

Accepted Answer

The answer of A sample of n = 25 scores...

Question 16

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?

Accepted Answer

The answer of If a sample of n = 16...

Question 17

With α = .01 the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ______.

Accepted Answer

Using a t-table or calculator with degrees of freedom (df) = n-1 = 16-1 = 15, we find the critical t-value for a two-tailed test with α = .01 is ±2.947. Therefore, the correct answer is option C.

Question 18

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

Accepted Answer

The answer of The results of a hypothesis test are...

Question 19

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

Accepted Answer

The t statistic is used to estimate the value for an unknown population mean.

Question 20

A sample of n = 16 scores produces a t statistic of t = 2.00.If the sample is used to measure effect size with r², what value will be obtained for r²?

Accepted Answer

The formula for calculating effect size using r (Cohen's r) from a t-test is r = sqrt(t^2 / (t^2 + df)), where df (degrees of freedom) is n - 1 for a one-sample t-test. Here, n = 16, so df = 15. Plugging in the values, r = sqrt(2^2 / (2^2 + 15)) = sqrt(4 / 19), which corresponds to choice D.

Quiz 9: Introduction to the T Statistic