Imagine you are looking to test whether students in an online section of a particular course get higher grades than students in the in-person section. You take a sample of 48 students in the online class and 48 students in the in-person class. You test this using a t-test of students’ final grades. Students in your sample of the online class receive an average grade of 83 with a standard deviation of 6. Students in the in-person class receive an average grade of 75 with a standard deviation of 10. What is the estimated standard error of the difference between means?

(If you miss any of the numerical questions, you can upload a file in the homework 5 file upload assignment showing your work for potential partial credit)

Question

Imagine you are looking to test whether students in an online section of a particular course get higher grades than students in the in-person section. You take a sample of 48 students in the online class and 48 students in the in-person class. You test this using a t-test of students’ final grades. Students in your sample of the online class receive an average grade of 83 with a standard deviation of 6. Students in the in-person class receive an average grade of 75 with a standard deviation of 10. What is the estimated standard error of the difference between means?

(If you miss any of the numerical questions, you can upload a file in the homework 5 file upload assignment showing your work for potential partial credit)

BlackTom AI · Accepted Answer

We begin by identifying the formula for the standard error of the difference between two independent sample means. When comparing online versus in-person class final grades, the estimated standard error (SE) of the difference is SE = sqrt( (s1^2 / n1) + (s2^2 / n2) ).

First, list the given values: sample sizes n1 = 48 and n2 = 48; sample standard deviations s1 = 6 and s2 = 10.

Compute each component:
- s1^2 / n1 = 6^2 / 48 = 36 / 48 = 0.75.
- s2^2 / n2 = 10^2 / 48 = 100 / 48 ≈ 2.083333.

Next, add these components to get the variance of the difference:
- 0.75 + 2.083333 ≈ 2.833333.

Finally, take the square root to obtain the standard error:
- SE = sqrt(2.833333) ≈ 1.683.

Note on the context: this SE is the estimate used in the t-test by incorporating the variability of both sample means based on their respective spreads and sample sizes. If you were to perform a two-sample t-test assuming independent samples with unequal variances, a slightly different approach (Welch’s t-test) would adjust the SE calculation, but for the standard pooled or basic formulation here, the above computation yields about 1.683. Since no answer options were provided in this prompt, I’ve shown the full calculation path step by step to aid understanding of how the value arises.

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