Question

To investigate whether there is a difference in student mark achievement between an "in-person" class and a class delivered online, two sections of an introductory calculus course were followed. One section was delivered in person, and the other section was completely delivered online. Both classes were instructed by the same professor, and students could only be enrolled in one section at a time.

After the final exam was completed, n_in-person = 18 students were randomly chosen from the in-person lecture section, and n_online = 14 students were randomly chosen from the online lecture section. The final exam scores, in %, were observed for each chosen student.

(a) Compute the 94% confidence interval for μ_in-person - μ_online, where μ_in-person represents the population mean for the in-person section, and μ_online represents the population mean for the online section. Provide your answer to at least two decimal places.

(b) According to the confidence interval obtained in part (a), is there a significant difference between the two sections?

A. Not enough information to infer, since the truth can never be known.
B. No.
C. Yes.

(c) Could this data and experimental design ever be considered a matched pairs test?

A. Yes, if the sample sizes happened to be the same.
B. Not enough information to determine.
C. No.

Please provide the a

Answer 1

To compute the 94% confidence interval for μ_in-person - μ_online, calculate the margin of error and build the interval around the difference in sample means.

Step-by-step explanation:

To compute the 94% confidence interval for μin-person - μonline, we need to calculate the margin of error and then build the interval around the difference in sample means.

Step 1:

Calculate the standard error (SE), which is the standard deviation divided by the square root of the sample size for each group.

SE

in-person

= standard deviation

in-person

/ √(n

in-person

)

SE

online

= standard deviation

online

/ √(n

online

)

Step 2:

Calculate the margin of error (ME) by multiplying the critical value (z*) with the calculated standard error. The critical value for a 94% confidence interval is approximately 1.882.

ME = z* x SE