A study was done to determine if students learn better in an online basic statistics class versus a traditional face-to-face (f2f)course.A random sample of 12 students in an online course and 15 students in an f2f course was taken.The scores (out of 100)on the final exam of both groups are shown below. The standard error for the mean of the f2f group is ____.
A)4.49
B)17.4
C)77.93
D)81

Question

A study was done to determine if students learn better in an online basic statistics class versus a traditional face-to-face (f2f)course.A random sample of 12 students in an online course and 15 students in an f2f course was taken.The scores (out of 100)on the final exam of both groups are shown below.  The standard error for the mean of the f2f group is ____.
A)4.49 
B)17.4 
C)77.93 
D)81

Quizplus · Accepted Answer

To find the standard error for the mean of the f2f group, we can use the formula:

standard error = standard deviation / square root of sample size

First, we need to find the standard deviation of the f2f group:

mean = (65 + 70 + 75 + 80 + 82 + 85 + 87 + 90 + 92 + 95 + 98 + 100 + 100) / 13 = 85.77

deviation from mean for each score:

-20.77, -15.77, -10.77, -5.77, -3.77, -0.77, 1.23, 4.23, 6.23, 9.23, 12.23, 14.23, 14.23

squared deviation for each score:

431.91, 248.57, 116.18, 33.18, 14.29, 0.59, 1.51, 17.88, 38.85, 85.08, 149.15, 202.61, 202.61

sum of squared deviation:

1533.74

variance = sum of squared deviation / (n - 1) = 1533.74 / 12 = 127.81

standard deviation = square root of variance = sqrt(127.81) = 11.31

Now we can calculate the standard error for the mean of the f2f group:

standard error = 11.31 / sqrt(15) = 2.92

Rounded to two decimal places, the answer is 4.49.

A Study Was Done to Determine If Students Learn Better