|
STAtistics / Mr. Hansen |
Name:
_________________________ |
Test through Chapter 11
|
1. |
A trove of fossils of
ancient dogs reveals that the males of the species appear to have longer
tibiae (leg bones) than the females. Here are some data: |
|
|
|
|
|
Male tibiae (cm): 22, 15,
12, 13, 19, 16 |
|
|
Female tibiae (cm): 18, 16,
11, 9, 12, 11 |
|
|
|
|
|
Is there evidence that the
true mean for males exceeds the true mean for females? Use an alpha level of
0.05. Show work. |
|
2. |
A quality-control officer
for Hansen Widgets, Inc., will reject any lot of widgets
whose sample mean diameter (using a random sample of 15 from a large lot) is
less than 5 cm. Widget diameters are normally distributed. |
|
|
|
|
(a) |
If the sample mean is 5.2
cm, with s = 0.5 cm, is there any evidence
that the true mean diameter is different from 5 cm? Show work. |
|
|
|
|
(b) |
If the true population mean
is 5 cm, compute the probability that the quality-control officer will commit
a Type I error on a given future lot. NO
WORK IS REQUIRED for part (b). |
|
3. |
In a demonstration of
purported ESP ability, 40 people who claim to have psychic ability are
competing against 40 randomly chosen “muggles” (people
with no special ability). The competition involves trying to guess which of
three possible symbols is being displayed by a judge in a sealed room out of
sight of the competitors. At the end of the competition, the score is psychics 15, muggles 11. |
|
|
|
|
|
Is there evidence that the
true probability with which the psychics can guess the secret symbol exceeds
that for the muggles? Show work. |
|
4. |
In #3, is there evidence that
the true probability with which the psychics can guess the secret symbol
exceeds what chance alone would predict? Show work. |