Sarah
Butler – Teaching Assistant
March
14 2001
Name:
__________________________________________________
Please
answer all questions and show all work.
1.
(15 pts)The table below shows the numbers of voters in the US by age based on a
recent census.
|
Age of Voters Frequency (millions) |
||
|
18-20 |
10.8 |
|
|
21-24 |
13.9 |
|
|
25-34 |
40.1 |
|
|
35-44 |
43.3 |
|
|
45-64 |
53.7 |
|
|
65-84 |
31.9 |
|
a)
(3)Find
the probability that a voter chosen at random is between 21 and 24 years of
age.
b)
(3)
Find the probability that a voter chosen at random is between 35 and 64 years
of age.
c)
(3)
Find the probability that a voter chosen at random is less than 65 years of
age.
d)
(6)
Find the mean age of this voting population.
a) 13.9/193.7 = 0.072
b) (43.3+53.7)/193.7 = 0.501
c) 1- 31.9/193.7 = 0.835
d) 44.98
Name:
__________________________________________________
2.
(20
pts) For each of the terms in the left column is the definition on the left
correct. If not suggest a suitable correction.
a
The
probability of accepting a true null hypothesis
incorrect:
maximum acceptable probability of rejecting a true H0
c2 A symmetric probability distribution used to
test for differences between means for small samples
incorrect:
asymmetric, testing for sigma2 or goodness of fit test
.
s The population variance
incorrect:
sample standard deviation
N(0,1) The standard normal
distribution
correct
r2 the
correlation coefficient between two
sampled variables
incorrect:
coefficient of determination
Binomial
distribution A probability
distribution for the number of successes in n independent trials
correct
Central
limit theorem A theorem that says that
95% of all observations lie within 2 standard deviations of the mean.
incorrect:
for a sample with n>30 for any distribution, the mean follows a
normal
distribution
Box
and whisker diagram A diagram showing
the median, quartiles, range and mean of a sample
incorrect:
does NOT include the mean
Confidence
interval The range of values around
the population mean (or any population parameter) that is expected to contain
the sample mean with some pre-chosen probability.
incorrect:
range of values around the SAMPLE mean or SAMPLE
STATISTIC
tc The cutoff
for the rejection region in a normal probability distribution
incorrect:
for the t probability distribution
Name:
__________________________________________________
3.(30
pts)The table below shows reading test scores for two groups of third graders.
The first group of 21 students participated in directed reading activities for
10 weeks (column 1). The second group of 23 students followed the same
curriculum without directed reading activities (column 2). Both classes took
the same reading test after their curriculum.
|
Reading scores test |
|
|
24 |
42 |
|
43 |
43 |
|
58 |
55 |
|
71 |
26 |
|
43 |
62 |
|
49 |
37 |
|
61 |
33 |
|
44 |
41 |
|
67 |
19 |
|
49 |
54 |
|
53 |
20 |
|
56 |
85 |
|
59 |
46 |
|
52 |
10 |
|
62 |
17 |
|
54 |
60 |
|
57 |
53 |
|
33 |
42 |
|
46 |
55 |
|
43 |
28 |
|
57 |
48 |
|
|
37 |
|
|
42 |
|
51.47619 |
41.52174 |
|
Mean x1 |
Mean x2 |
|
121.1619 |
294.0791 |
|
s12 |
s22 |
a. (10) Draw a stem and leaf diagram for each population. Do the populations appear to be normally distributed?
b. (10) Assuming the populations are normally distributed, test for equality of variance between the two populations for significance level a=0.10.
c. (10) Given the populations are normally distributed test the claim that the performance of the third grade students with the directed reading activities (population 1 above) performed better on the test than those without the activities at significance level a=0.05. Interpret the results of the test.
Name: __________________________________________________
key: 2|1 = 21
population 1: population
2:
2|4 1|0
7 9
3|3 2|0
6 8
4|3 3 3 4 6 9 9 3|3
7 7
5|2 3 4 6 7 7 8 9 4|1
2 2 2 3 6 8
6|1 2 7 5|3
4 5 5
7|1 6|0
2
7|
8|5
Population 1 appears to be
normally distributed, while population two does not
b)
H0: sigma1
= sigma2 H0:
sigma1 not equal sigma2
F = 2.427, F0 ~ 2.10 (between 2.12 and 2.08), reject H0
c) H0: mu1<=
mu2 mu1>mu2
t = 2.31, t0 1.725,
reject H0
Name: __________________________________________________
4. (15 pts.) 52% of adults say chocolate chip is their favorite cookie. A community bake sale has prepared 350 chocolate chip cookies. The bake sale attracts 650 adult customers (what no kids?) and each buys one cookie (their favorite). What is the probability there will not be enough chocolate chip cookies?
This is a binomial problem,
X~bin(650,0.52) ~ N(338,12.74) mu=np, sigma=SQRT(npq)
P(X>350) = P(X>=350.5) =
P(Z>(350.5-338)/12.74) = P(Z>0.981) = 1-P(Z<0.981) = 0.1611
5. (20 pts.) The following table gives the median age in years of cars and trucks on the road in the US for seven different years.
|
Median age of vehicles on road |
||
|
Cars, x |
Trucks, y |
|
|
8.1 |
7.8 |
|
|
7.7 |
7.6 |
|
|
6.5 |
6.5 |
|
|
6.9 |
7.6 |
|
|
6 |
6.3 |
|
|
5.4 |
5.8 |
|
|
4.9 |
5.9 |
|
a. (5) Draw a scatterplot for these data. Label both axes. What kind of relationship is there between the median age of cars and trucks?
b. (5) Compute the correlation coefficient between the median age of cars and trucks on the road.
c. (5) Test the null hypothesis that the population correlation coefficient r=0 with a=0.05.
d. (5) Find the coefficient of determination of these data.
a) r = 0.942
b) t = 6.27, t0 = 2.015,
reject H0
c) r2 = 0.9422
= 0.887