Q: If the calculated $p$-value for an independent-samples t test is $0.03$, how should the result be reported?

$p < 0.05$, there is a significant difference between means

Q: Which of the following is a correct interpretation of a large effect size ($d = 0.8$) in an independent-samples t test?

There is a substantial difference between the two group means

Question 1

Which of the following best describes the purpose of an independent-samples t test?

Accepted Answer

To compare two means in a between-groups design

Question 2

In the context of the wine study, what is the null hypothesis ($H_0$) for an independent-samples t test?

Accepted Answer

$H_0: \mu_1 = \mu_2$

Question 3

Which of the following is an assumption of the independent-samples t test?

Accepted Answer

Participants are assigned to only one condition

Question 4

What is the formula for the pooled variance ($s^2_{pooled}$) in an independent-samples t test?

Accepted Answer

$s^2_{pooled} = \frac{df_X}{df_{total}} s^2_X + \frac{df_Y}{df_{total}} s^2_Y$

Question 5

Which of the following steps is NOT part of the process for calculating an independent-samples t test?

Accepted Answer

Calculate the mean difference for matched pairs

Question 6

Given the following sample means and standard errors: $M_X = 10$, $M_Y = 8$, $S_{difference} = 1.5$, what is the value of the t statistic?

Accepted Answer

$t = \frac{10 - 8}{1.5} = 2.67$

Question 7

Which formula is used to calculate Cohen's $d$ for effect size in an independent-samples t test?

Accepted Answer

$d = \frac{(M_X - M_Y) - (\mu_X - \mu_Y)}{s_{pooled}}$

Question 8

A researcher calculates a 95% confidence interval for the difference between two means and finds the interval does not include zero. What does this imply?

Accepted Answer

There is a statistically significant difference between the two means

Question 9

Which of the following best describes the Bayesian approach to data analysis?

Accepted Answer

It incorporates prior beliefs and probabilities into statistical inference

Question 10

If the calculated $p$-value for an independent-samples t test is $0.03$, how should the result be reported?

Accepted Answer

$p < 0.05$, there is a significant difference between means

Question 11

Which of the following is a correct interpretation of a large effect size ($d = 0.8$) in an independent-samples t test?

Accepted Answer

There is a substantial difference between the two group means

Question 12

Which formula is used to calculate the standard error of the difference between means ($S_{difference}$)?

Accepted Answer

$S_{difference} = \sqrt{S^2_{M_X} + S^2_{M_Y}}$

Question 13

A psychologist wants to compare the happiness scores of two independent groups. Which statistical test should they use?

Accepted Answer

Independent-samples t test

Question 14

Which of the following is NOT a step in calculating a confidence interval for an independent-samples t test?

Accepted Answer

Calculate the mean of the pooled variances

Question 15

If the participants in a study were not randomly selected, what is a key limitation when interpreting the results of an independent-samples t test?

Accepted Answer

The findings may not generalize to the broader population

Question 16

Which of the following best describes the comparison distribution for an independent-samples t test?

Accepted Answer

A distribution of differences between means

Question 17

A researcher finds $t(18) = 2.10, p = 0.049$ for an independent-samples t test. What is the correct interpretation?

Accepted Answer

There is a statistically significant difference between the two groups

Question 18

Which of the following is a real-world example where an independent-samples t test would be appropriate?

Accepted Answer

Comparing the average test scores of students taught with two different teaching methods

Independent-Samples t Test: Statistical Methods for Comparing Two Means

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