A First Course in Differential Equations with Modeling Applications (MindTap Course List)
11th Edition
ISBN: 9781305965720
Author: Dennis G. Zill
Publisher: Cengage Learning
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Textbook Question
Chapter 9.1, Problem 21E
Answer the question “Why not?” that follows the three sentences after Example 2 on page 372.
TABLE 9.1.3 Improved Euler’s Method with h = 0.1
TABLE 9.1.4 Improved Euler’s Method with h = 0.05
A brief word of caution is in order here. We cannot compute all the values of
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1a. For the following data:
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2 0
3 1
7 4
5 6
4 6
3 1
Draw the scatterplot (MUST SHOW WORK FOR THIS PROBLEM)
Group of answer choices
a. yes
b. no
1b. Using the dataset given in problem 14, test the hypothesis that there is a significant positive relationship between the # of siblings an individual grows up with and the number of children they eventually have. Use α = .05.
Which of the following accurately represents the null and alternative hypotheses? (MUST SHOW WORK FOR THIS PROBLEM)
Group of answer choices
a. H0: ρ ≤ 0, H1: ρ > 0
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The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.
a. Use ? = .01 to test the hypotheses for the model y = ?0 + ?1?1 + ?2?2 + ?, where:
H0 : ?1 = ?2 = 0
Ha : ?1 and/or ?2 ≠0
Compute the F test statistic (to 2 decimals).
b. Use ? = .05 to test the significance of ?1. Compute the t test statistic (to 2 decimals).
c. Use ? = .05 to test the significance of ?2. Compute the t test statistic (to 2 decimals).
d. The owner plans to spend (in $1000s) $4.5 on television advertising and $3.6 on newspaper advertising. What is the expected revenue (in $1000s) for this advertising combination (to the nearest whole number)?
QUESTION 23
Assuming all other factors are held constant, if the df value for a two-tailed t-test with α = .05 were increased from df = 6 to df = 20, what would happen to the critical values for t?
a.
The critical values would further from t = 0.
b.
The critical values would not change.
c.
The critical values would move closer to t = 0.
d.
This is impossible to determine without more information.
Chapter 9 Solutions
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - Prob. 4ECh. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - Prob. 6ECh. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - In Problems 110 use the improved Eulers method to...
Ch. 9.1 - Consider the initial-value problem y′ = (x + y –...Ch. 9.1 - Consider the initial-value problem y = 2y, y(0) =...Ch. 9.1 - Repeat Problem 13 using the improved Eulers...Ch. 9.1 - Repeat Problem 13 using the initial-value problem...Ch. 9.1 - Repeat Problem 15 using the improved Euler’s...Ch. 9.1 - Consider the initial-value problem y = 2x 3y + 1,...Ch. 9.1 - Repeat Problem 17 using the improved Euler’s...Ch. 9.1 - Repeat Problem 17 for the initial-value problem y′...Ch. 9.1 - Repeat Problem 19 using the improved Euler’s...Ch. 9.1 - Answer the question Why not? that follows the...Ch. 9.2 - Use the RK4 method with h = 0.1 to approximate...Ch. 9.2 - Assume that (4). Use the resulting second-order...Ch. 9.2 - In Problems 3–12 use the RK4 method with h = 0.1...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 3–12 use the RK4 method with h = 0.1...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - If air resistance is proportional to the square of...Ch. 9.2 - Consider the initial-value problem y = 2y, y(0) =...Ch. 9.2 - Repeat Problem 16 using the initial-value problem...Ch. 9.2 - Consider the initial-value problem y′ = 2x – 3y +...Ch. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.3 - Prob. 1ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - In Problems 58 use the Adams-Bashforth-Moulton...Ch. 9.4 - Use Eulers method to approximate y(0.2), where...Ch. 9.4 - Use Euler’s method to approximate y(1.2), where...Ch. 9.4 - Prob. 3ECh. 9.4 - In Problems 3 and 4 repeat the indicated problem...Ch. 9.4 - Prob. 5ECh. 9.5 - In Problems 110 use the finite difference method...Ch. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - In Problems 1 – 10 use the finite difference...Ch. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - The electrostatic potential u between two...Ch. 9.5 - Prob. 13ECh. 9 - In Problems 14 construct a table comparing the...Ch. 9 - In Problems 14 construct a table comparing the...Ch. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RE
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The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
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Suppose you fit the first-order model
y=β0+β1x1+β2x2+β3x3+β4x4+β5x5+ε
to
n=30
data points and obtain
SSE=0.33
and
R2=0.93.
Complete parts a and
b.
Question content area bottom
Part 1
a. Do the values of SSE and
R2
suggest that the model provides a good fit to the data? Explain.
A.
No. Since
R2=0.93
is close to 1, this indicates the model does not provide a good fit. Also,
SSE=0.33
is fairly small, which indicates the model does not provide a good fit.
B.
There is not enough information to decide.
C.
Yes. Since
R2=0.93
is close to 1, this indicates the model provides a good fit. Also,
SSE=0.33
is fairly small, which indicates the model provides a good fit.
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A developmental psychologist working in the area of suggestion asked a sample of children to solve as many problems as they could in 15 minutes. Half of the children are told that this is a problem-solving task and the other half are told that this is just a time-filling task. The psychologist is interested in the impact of the suggestion on problem solving. What can be concluded with an α of 0.01? Below is the data for the number of problems solved.
A) Condition 1 = Condition 2=
B) critical value= test statistic = Reject or Fail to Reject
C)Compute the corresponding effect size(s) and indicate magnitude(s)
d= / magnitude=
r2 = / magnitude=
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Use the following linear regression equation to answer the questions.
(d) x1 = 1.0 + 3.9x2 – 8.4x3 + 2.4x4
Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?Suppose x2 increased by 2 units. What would be the expected change in x1?Suppose x2 decreased by 4 units. What would be the expected change in x1?(e) Suppose that n = 8 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.468. Construct a 90% confidence interval for the coefficient of x2. (Use 2 decimal places.)
lower limit
upper limit
(f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.)
t
t critical ±
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