At a large university the Biomedical Engineering faculty dec

At a large university, the Biomedical Engineering faculty decides to teach a course on robot intelligence using two different methods, one an existing method and the other a method using new strategies. The faculty randomly selects two sections of students who are scheduled to take this course. One section is taught using the existing method while the other uses the new method. At the end of the semester, both sections are given the same test. Their test scores produce the following summary statistics:

Solution

a)
CI = x1 - x2 ± Z a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x1)=79
Standard deviation( sd1 )=5.477
Sample Size(n1)=49
Mean(x2)=86
Standard deviation( sd2 )=6.3246
Sample Size(n12=36
CI = [ ( 79-86) ±Z a/2 * Sqrt( 29.997529/49+40.00056516/36)]
= [ (-7) ± Z a/2 * Sqrt( 1.7233) ]
= [ (-7) ± 1.96 * Sqrt( 1.7233) ]
= [-9.573 , -4.427]
b)
AT 98% CI, 2 sided C.I
CI = [ ( 79-86) ±Z a/2 * Sqrt( 29.997529/49+40.00056516/36)]
= [ (-7) ± Z a/2 * Sqrt( 1.7233) ]
= [ (-7) ± 2.326 * Sqrt( 1.7233) ]
= [-10.0535 , -3.9465]

AT 98% CI, one sided
CI = [ ( 79-86) ±Z a/2 * Sqrt( 29.997529/49+40.00056516/36)]
= [ (-7) ± Z a/2 * Sqrt( 1.7233) ]
= [ (-7) ± 2.05 * Sqrt( 1.7233) ]
= [-9.6911,-4.3088]