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Stat 1 Sec. 6&12
T-H Final
Name _______________
Label & Scale Axes
Dr. Etterbeek
Fall Ã¢â‚¬Ëœ21
Ã¢Ë†â€˜=
1. When bears were anesthetized, researchers measured the diameter (in inches) of the
bearsÃ¢â‚¬â„¢ chests and weighed the bears (in pounds). The results are shown in the table
below.
x Chest (in)
26
45
54
49
41
49
44
19
y Weight (lb)
90
304
446
348
321
395
259
58
yÃŒâ€š
RESID
(14)
a. Find the regression equation for yÃŒâ€š in terms of x.
b. Identify the predictor and response variables and give their dimensions.
c. Find and interpret the slope of the regression line in context.
d. Graph the observations and the regression line.
1
1. (cont.)
e. Use your graph to estimate the weight of a bear with a chest size of 40 inches.
f. Use the regression equation to estimate the weight of a bear with a chest size
of 40 inches. (Show your work.)
g. Complete the table giving the estimated weight and the residuals.
h. Find the correlation coefficient.
i. Graph the residuals.
j. Use the results of parts (h) and (i) to determine the appropriateness of a linear
model for these data.
2
2. The urn contains 1 ball numbered one, 2 balls numbered two , 3 balls numbered
three, and 4 balls numbered four as shown in the figure below.
1
2
2
3
3
4
4
4
3
4
A ball is drawn at random from the urn, and the random variable X equals the number
on the ball.
(6)
a. Complete the frequency table for the random variable X .
x
Frequency
b. Complete the probability table for the random variable X .
x
Pr(x)
xPr x
()
x Pr ( x )
2
c. Find and interpret the mean of X. (Show your work.)
d. Find the standard deviation of X. (Show your work.)
3
3. The data in the table below gives the daily costs of 15 randomly selected families of
four to spend one day at an American amusement park.
256
221
209
212
178
195
218
208
207
189
152
179
172
184
181
In this problem you will be computing a confidence interval for the average cost of a
family of four to spend one day at an American amusement park. You may assume
that the daily costs for all families of four at an amusement park are normally
distributed.
(10)
a. For this situation define the:
Population X:
Estimated Parameter:
Estimator:
Population X :
b. Construct a 99% confidence interval for the population mean.
i. Interval and Conditions
Interval:
Conditions:
4
3. (cont.)
ii. Computation:
iii. Interpretation
Confidence Interval:
Confidence Level:
4. The data shown in the table below gives the total weights of garbage (in pounds) for
one week for 32 randomly selected households in the Providence area. It is known
that the standard deviation for all of the weekly weight of garbage in the Providence
area is 8.4 lbs
10.76
19.98
27.60
38.11
27.90
21.90
21.83
14.95
33.27
35.54
44.44
45.17
33.07
10.35
44.44
24.13
37.60
38.96
17.17
31.60
22.22
42.99
20.20
36.80
19.02
15.43
20.71
17.01
23.67
19.13
20.99
21.18
In this problem you will be testing an hypothesis concerning the average weekly
weight of household garbage (in pounds) in the Providence area. Ã¢Ë†â€˜ x = 858.12 )
(10)
a. For this situation define the:
Population X:
Hypothesized Parameter:
Estimator:
Population X :
5
4. (cont.)
b. Can we conclude at the 0.05 level of significance that the mean weight of
household garbage for one week in the Providence area is different
from 30 lb
i. Hypotheses:
H0:
Ha:
ii. Conditions:
iii. Computation:
0
iv. Conclusion:
6
Table of t distribution.
7