Question

Students may choose between a 3-semester-hour physics course without labs and a 4-semester-hour course with labs. The final written examination is the same for each section. If 12 students in the section with labs made an average grade of 84 with a standard deviation of 4, and 18 students in the section without labs made an average grade of 77 with a standard deviation of 6, find a 99% confidence interval for the difference between the average grades for the two courses. Assume the populations to be approximately normally distributed with equal variances.

Answer 1

Solution

Here, given that,

For students with labs,

Sample size, n₁ = 12

Sample mean,  = 84

Sample standard deviation, s₁ = 4

And, for students without labs,

Sample size, n₂ = 18

Sample mean,  = 77

Sample standard deviation, s₂ = 6.

Now, a general Confidence lnterval (CI) for the difference in means with equal population variances is given by

, 

where, ,

And, 

Here, 

Now, the pooled estimate of the standard deviation is given by

So, Standard Error is given by

Now, level of significance,  = 1-0.99 = 0.01.

So, we have,

, using t table with row, df=28 and column under one-tailed probability of 0.005.

Therefore, the 99% Confidence Interval for the difference between the average grades for the two courses is given by