Question 1

Which of the following best describes the purpose of the single-sample t test?

Accepted Answer

To determine if a sample mean is significantly different from a known population mean when the population standard deviation is unknown.

Question 2

What happens to the shape of the t distribution as the sample size increases?

Accepted Answer

It becomes narrower and taller, approaching the normal distribution.

Question 3

Given a sample of five scores: 8, 12, 16, 12, 14, what is the sample mean $M$?

Accepted Answer

$M = \frac{8+12+16+12+14}{5} = 12.4$

Question 4

Which formula is used to estimate the population standard deviation from a sample?

Accepted Answer

$s = \sqrt{\sum (X - M)^2 / (N-1)}$

Question 5

A researcher collects a sample of $N=5$ and calculates $s=2.97$. What is the standard error $S_M$?

Accepted Answer

$S_M = \frac{2.97}{\sqrt{5}} = 1.33$

Question 6

If the sample mean $M = 12.4$, the population mean $\mu_M = 11$, and the standard error $S_M = 1.33$, what is the value of the t statistic?

Accepted Answer

$t = \frac{12.4 - 11}{1.33} = 1.05$

Question 7

How are degrees of freedom ($df$) calculated for a single-sample t test?

Accepted Answer

$df = N - 1$

Question 8

Which of the following is NOT an assumption of the single-sample t test?

Accepted Answer

The population standard deviation is known.

Question 9

A counseling center wants to know if clients who sign a contract to attend at least 10 sessions have a different mean attendance than the general population. Which test should they use?

Accepted Answer

Single-sample t test

Question 10

If the calculated t statistic is 2.873 and the critical value for $df=4$ at the 0.05 level (two-tailed) is 2.776, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 11

What does a 95% confidence interval mean in the context of repeated sampling?

Accepted Answer

The interval will contain the population mean 95% of the time if we repeatedly sample.

Question 12

Which formula is used to calculate effect size (Cohen's d) for a single-sample t test?

Accepted Answer

$d = \frac{M - \mu}{s}$

Question 13

Which step in hypothesis testing involves determining the characteristics of the comparison distribution?

Accepted Answer

Step 3

Question 14

Why do we use $N-1$ in the denominator when calculating sample standard deviation?

Accepted Answer

To correct for bias in estimating the population variance from a sample.

Question 15

A sample of $N=5$ yields $M=7.8$, $\mu_M=4.6$, and $S_M=1.114$. What is the t statistic?

Accepted Answer

$t = \frac{7.8 - 4.6}{1.114} = 2.873$

Question 16

If the sample mean is 7.8 and the 95% confidence interval is [4.71, 10.89], what is the margin of error?

Accepted Answer

3.09

Question 17

Which of the following is a correct null hypothesis for a single-sample t test?

Accepted Answer

$H_0: \mu_1 = \mu_2$

Question 18

Which real-world scenario would most appropriately use a single-sample t test?

Accepted Answer

Comparing the average blood pressure of a group of patients to the known average for the general population when the population standard deviation is unknown.

The Single-Sample t Test: Concepts, Calculations, and Interpretation

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