In: Statistics and Probability
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.
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