Question

A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers, familiar with both languages, are asked to code a standard function in both languages, and the time (in minutes) is recorded. The data follow:

Programmer	Time
	Design Language 1	Design Language 2
1	17	18
2	17	14
3	21	20
4	14	11
5	18	23
6	24	21
7	15	10
8	14	13
9	21	19
10	23	24
11	13	15
12	18	19

a) Is the assumption that the difference in coding time is normally distributed reasonable?

(b) Find a 95% confidence interval on the difference in mean coding times. Is there significant indication that one design language is preferable at a 5% significance level?

Answer 1

(a) Yes, the assumption that the difference in coding time is normally distributed is reasonable, because the sample size is fairly big for the analysis to be carried out.

(b) x = coding time for Language 1, y = coding time for Language 2.
Now, d = difference in coding time between Language 1 and Language 2 = x - y.
Also, = mean difference in coding time between Language 1 and Language 2.
The value of "d" for all the 12 programmers is = (-1, 3, 1, 3, -5, 3, 5, 1, 2, -1, -2, -1).


Since the confidence interval contains 0 within itself, we can say that there is no significant indication that one design language is preferable at 5% significance level.