Worksheet 5 9/03/08
Problem 1. Before they attend college, every Martian takes the MAT (Martian Aptitude
Test). An SRS of Martian high school students is collected, and the results are below:
33.2 31.9 32.6 26.5 33.3
32.3 33.0 32.0 30.5 32.7
23.0 30.9 32.7 33.7 32.3
24.1 30.2 31.3 28.7 31.9
The population standard deviation of MAT scores is σ= 3.
(a) We know for the SAT, that the scores are approximately normal. From this sample,
does it appear that MAT scores are also approximately Normally distributed? Make a
stemplot to check.
23 |0
24 |1
25 |
26 |5
27 |
28 |7
29 |
30 |259
31 |399
32 |033677
33 |0237
Actually, appears a bit left skewed. (However, the overall distribution may be Normal)
(b) Assuming that it is in fact Normal, calculate a 90% confidence interval for the mean
MAT score.
Calculating, we get ¯x= 30.84. For 90% confidence z∗= 1.645. There are 20 scores, so
our confidence interval is
30.84 ±1.645 3
√20 = 30.84 ±1.10 = (29.74,31.94)
(c) What size sample do we need to collect to get the margin of error down to .5?
We use the formula n=z∗σ
m2where mis margin of error.
n=(1.645)(3)
.52
= 97.417
Since we can’t have a partial person, we round this up to 98.
