3.56 Predicting heights of spruce trees. In forestry, the 1o b diameter of a tree at breast height (which is fairly easy to measure) is used to predict the height of the tree (a difficult measurement to obtain). Sil. viculturists working in British Columbia's boreal forest conducted a series of spacing trials to predict the heights of several species of trees. The data in the next table are the breast height diameters (in centimeters) and heights (in meters) for a sample boat of 36 white spruce trees. (a) Construct a scatterplot for the data. (b) Assuming the relationship between the vari- ables is best described by a straight line, use the method of least squares to estimate the ELU y-intercept and slope of the line. al for a limt on Its wi you nolega te A Complete Example 135 ice samples, ntout of the (c) Plot the least squares line on your scatterplot. (d) Do the data provide sufficient evidence to AtabogireAb s indicate that the breast height diameter x con- tributes information for the prediction of tree = .05. (e) Use your least squares line to find a 90% con- fidence interval for the average height of white spruce trees with a breast height diameter of 20 cm. Interpret the interval. WHITESPRUCE %confidence ex, E(y), for spreadsheet. is interval. BREAST HEIGHT BREAST HEIGHT DIAMETER HEIGHT DIAMETER HEIGHT y, m x, cm e y, mnoueCA х, ст height y? Test using a = 20.0 16.6 15.5 18.9 18.8 16.8 15.5 19.4 20.0 16.9 16.3 20.2 13.7 e Journal of (June 2000) 103). 20.0 27.5 21.4 29.8 20.2 20.3 19.2 19.8 18.0 17.8 22.9 19.8 FHWABRIDGE 20.3 20.0 22.0 14.1 ES 10.1.S 5.80. or the mean n the fifth " Interpret 18.5 12.1 3.57 Structurally deficient highway bridges. Refer to the data on structurally deficient highway bridges compiled by the Federal Highway Administration (FHWA), Exercise 3.21 (p. 108). Recall that for future planning and budgeting, the FHWA wants to estimate the total area of structurally deficient bridges in a state based on the number of defi- cient bridges. Use the results of the simple linear regression relating total area (y) to number of structurally deficient bridges (x) to find a 95% prediction interval for y when x = 350 bridges. Interpret the result. 19.2 22.3 8.0 23.6 20.7 17.4 18.4 18.9 17.8LA 11.4 ESS 14.4 a.er 13.4 14.8 r the recall in the fifth " Interpret 13.3 22.7 18.5 20.6 17.3 16.6 21.5 14.8 19.0 19.2 16.1 12.9 sa and b. always be 17.8 E 20.7A 17.5 17.7 21.0 19.9 19.4 20.4 17.6 13.3 15.5 19.2 15.9 22.9 Source: Scholz, H., Northern Lights College, British Columbia. llol 8.A er to the
3.56 Predicting heights of spruce trees. In forestry, the 1o b diameter of a tree at breast height (which is fairly easy to measure) is used to predict the height of the tree (a difficult measurement to obtain). Sil. viculturists working in British Columbia's boreal forest conducted a series of spacing trials to predict the heights of several species of trees. The data in the next table are the breast height diameters (in centimeters) and heights (in meters) for a sample boat of 36 white spruce trees. (a) Construct a scatterplot for the data. (b) Assuming the relationship between the vari- ables is best described by a straight line, use the method of least squares to estimate the ELU y-intercept and slope of the line. al for a limt on Its wi you nolega te A Complete Example 135 ice samples, ntout of the (c) Plot the least squares line on your scatterplot. (d) Do the data provide sufficient evidence to AtabogireAb s indicate that the breast height diameter x con- tributes information for the prediction of tree = .05. (e) Use your least squares line to find a 90% con- fidence interval for the average height of white spruce trees with a breast height diameter of 20 cm. Interpret the interval. WHITESPRUCE %confidence ex, E(y), for spreadsheet. is interval. BREAST HEIGHT BREAST HEIGHT DIAMETER HEIGHT DIAMETER HEIGHT y, m x, cm e y, mnoueCA х, ст height y? Test using a = 20.0 16.6 15.5 18.9 18.8 16.8 15.5 19.4 20.0 16.9 16.3 20.2 13.7 e Journal of (June 2000) 103). 20.0 27.5 21.4 29.8 20.2 20.3 19.2 19.8 18.0 17.8 22.9 19.8 FHWABRIDGE 20.3 20.0 22.0 14.1 ES 10.1.S 5.80. or the mean n the fifth " Interpret 18.5 12.1 3.57 Structurally deficient highway bridges. Refer to the data on structurally deficient highway bridges compiled by the Federal Highway Administration (FHWA), Exercise 3.21 (p. 108). Recall that for future planning and budgeting, the FHWA wants to estimate the total area of structurally deficient bridges in a state based on the number of defi- cient bridges. Use the results of the simple linear regression relating total area (y) to number of structurally deficient bridges (x) to find a 95% prediction interval for y when x = 350 bridges. Interpret the result. 19.2 22.3 8.0 23.6 20.7 17.4 18.4 18.9 17.8LA 11.4 ESS 14.4 a.er 13.4 14.8 r the recall in the fifth " Interpret 13.3 22.7 18.5 20.6 17.3 16.6 21.5 14.8 19.0 19.2 16.1 12.9 sa and b. always be 17.8 E 20.7A 17.5 17.7 21.0 19.9 19.4 20.4 17.6 13.3 15.5 19.2 15.9 22.9 Source: Scholz, H., Northern Lights College, British Columbia. llol 8.A er to the
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Topic Video
Question
Problem 3.56
part a, b, c, d, e (95% confidence interval for part e)
Transcribed Image Text:3.56 Predicting heights of spruce trees. In forestry, the
1o b diameter of a tree at breast height (which is fairly
easy to measure) is used to predict the height of
the tree (a difficult measurement to obtain). Sil.
viculturists working in British Columbia's boreal
forest conducted a series of spacing trials to predict
the heights of several species of trees. The data in
the next table are the breast height diameters (in
centimeters) and heights (in meters) for a sample
boat of 36 white spruce trees.
(a) Construct a scatterplot for the data.
(b) Assuming the relationship between the vari-
ables is best described by a straight line, use
the method of least squares to estimate the
ELU
y-intercept and slope of the line.
al
for a
limt on Its wi
you
Transcribed Image Text:nolega te A Complete Example
135
ice samples,
ntout of the
(c) Plot the least squares line on your scatterplot.
(d) Do the data provide sufficient evidence to
AtabogireAb s indicate that the breast height diameter x con-
tributes information for the prediction of tree
= .05.
(e) Use your least squares line to find a 90% con-
fidence interval for the average height of white
spruce trees with a breast height diameter of
20 cm. Interpret the interval.
WHITESPRUCE
%confidence
ex, E(y), for
spreadsheet.
is interval.
BREAST HEIGHT
BREAST HEIGHT
DIAMETER
HEIGHT
DIAMETER
HEIGHT
y, m
x, cm e y, mnoueCA
х, ст
height y? Test using a =
20.0
16.6
15.5
18.9
18.8
16.8
15.5
19.4
20.0
16.9
16.3
20.2
13.7
e Journal of
(June 2000)
103).
20.0
27.5
21.4
29.8
20.2
20.3
19.2
19.8
18.0
17.8
22.9
19.8
FHWABRIDGE
20.3
20.0
22.0
14.1 ES
10.1.S
5.80.
or the mean
n the fifth
" Interpret
18.5
12.1
3.57 Structurally deficient highway bridges. Refer to
the data on structurally deficient highway bridges
compiled by the Federal Highway Administration
(FHWA), Exercise 3.21 (p. 108). Recall that for
future planning and budgeting, the FHWA wants
to estimate the total area of structurally deficient
bridges in a state based on the number of defi-
cient bridges. Use the results of the simple linear
regression relating total area (y) to number of
structurally deficient bridges (x) to find a 95%
prediction interval for y when x = 350 bridges.
Interpret the result.
19.2
22.3
8.0
23.6
20.7
17.4
18.4
18.9
17.8LA
11.4 ESS
14.4
a.er
13.4
14.8
r the recall
in the fifth
" Interpret
13.3
22.7
18.5
20.6
17.3
16.6
21.5
14.8
19.0
19.2
16.1
12.9
sa and b.
always be
17.8 E
20.7A
17.5
17.7
21.0
19.9
19.4
20.4
17.6
13.3
15.5
19.2
15.9
22.9
Source: Scholz, H., Northern Lights College, British
Columbia.
llol
8.A
er to the
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