Chapter 9: Introduction to t Statistics

Which of the following is a fundamental difference between the t statistic and a z-score?

a. The t statistic uses the sample mean in place of the population mean.

b. The t statistic uses the sample variance in place of the population variance.

c. The t statistic computes the standard error by dividing the standard deviation by n – 1 instead of dividing by n.

d. All of the above are differences between t and z.

b. The t statistic uses the sample variance in place of the population variance.

Which of the following terms is not required when using the t statistic?

a. n

b. σ

c. df

d. s or s² or SS

b. σ

How does the shape of the t distribution compare to a normal distribution?

a. The t distribution is flatter and more spread out, especially when n is small.

b. The t distribution is flatter and more spread out, especially when n is large.

c. The t distribution is taller and less spread out, especially when n is small.

d. The t distribution is taller and less spread out, especially when n is small

a. The t distribution is flatter and more spread out, especially when n is small

If a t statistic is computed for a sample of n = 4 scores with SS = 300, then what are the sample variance and the estimated standard error for the sample mean?

a. s² = 10 and s_M = 5

b. s² = 100 and s_M = 20

c. s² = 10 and s_M = 20

d. s²= 100 and s_M = 5

d. s² =100 and s_M = 5

A sample is selected from a population with μ = 40, and treatment is administered to the sample. If the sample variance is s² = 96, which set of sample characteristics has the greatest likelihood of rejecting the null hypothesis?

a. M = 37 for a sample of n = 16

b. M = 37 for a sample of n = 64

c. M = 34 for a sample of n = 16

d. M = 34 for a sample of n = 64

d. M = 34 for a sample of n = 64

A sample is selected from a population and a treatment is administered to the sample. If there is a 2-point difference between the sample mean and the original population mean, which set of sample characteristics has the greatest likelihood of rejecting the null hypothesis?

a. s² = 12 for a sample with n = 25

b. s² = 12 for a sample with n = 9

c. s² = 32 for a sample with n = 25

d. s² = 32 for a sample with n = 9

a. s² = 12 for a sample with n = 25

A researcher uses a sample of n = 10 to evaluate a treatment effect and obtains t = 3.00. If effect size is measured using the percentage of variance accounted for, then what value will be obtained for r²?

a. 9/18 = 0.50

b. 9/17 = 0.53

c. 3/12 = 0.25

d. 3/11 = 0.27

a. 9/18 = 0.50

What happens to measure of effect size such as r² and Cohen’s d as sample size increases?

a. They also tend to increase.

b. They tend to decrease.

c. Sample size does not have any great influence on measures of effect size.

d. The effect of sample size depends on other factors such as sample variance

c. Sample size does not have any great influence on measures of effect size.

Which set of factors would produce the narrowest confidence interval for estimating a population mean?

a. A large sample and a large percentage of confidence

b. A large sample and a small percentage of confidence

c. A small sample and a large percentage of confidence

d. A small sample and a small percentage of confidence

b. A large sample and a small percentage of confidence

The results of a hypothesis test are reported as follows: “t(20 = 2.70, p < .05.” Based on this report, how many individuals were in the sample?

a. 19

b. 20

c. 21

d. cannot be determined from the information provided

c. 21

A researcher selects a sample of n = 16 individuals from a population with a mean of μ = 75 and administers a treatment to the sample. If the research predicts that the treatment will increase scores, then what is the correct statement of the null hypothesis for a directional (one-tailed) test?

a. μ ≥ 75

b. μ > 75

c. μ ≤ 75

d. μ < 75

c. μ ≤ 75

A researcher is conducting a directional (one-tailed) test with a sample of n = 25 to evaluate the effect of a treatment that is predicted to decrease scores. If the researcher obtains t = -1.700, then what decision should be made?

a. The treatment has a significant effect with either α = .05 or α = .01.

b. The treatment does not have a significant effect with either α = .05 or α = .01.

c. The treatment has a significant effect with α = .05 but not with α = .01.

d. The treatment has a significant effect with α = .01 but not with α = .05

b. The treatment does not have a significant effect with either α = .05 or α = .01

A researcher rejects the null hypothesis with a regular two-tailed test using α = .05. If the researcher used a directional (one-tailed) test with the same data, then what decision would be made? 

a. Definitely reject the null hypothesis.

b. Definitely reject the null hypothesis if the treatment effect is in the predicted direction.

c. Possibly not reject the null hypothesis even if the treatment effect is in the predicted direction.

d. It is impossible to determine without more information.

b. Definitely reject the null hypothesis if the treatment effect is in the predicted direction.