The Practice of Statistics for AP - 4th Edition
The Practice of Statistics for AP - 4th Edition
4th Edition
ISBN: 9781429245593
Author: Starnes, Daren S., Yates, Daniel S., Moore, David S.
Publisher: Macmillan Higher Education
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Chapter 12.1, Problem 13E

(a)

To determine

To describe what this graph tells you about the relationship between these two variables.

(a)

Expert Solution
Check Mark

Explanation of Solution

In the question the researcher examined the weeds among the corn yields. Thus, the scatterplot is also given in the question for the variables used. Thus, by looking at the scatterplot we can say that,

Direction: Negative, because the scatterplot slopes downwards.

Form: Linear, because the points seem to roughly lie about a line.

Strength: Weak, because the points lie far apart.

Thus, the scatterplot suggest a weak negative linear relationship between the variables.

(b)

To determine

To find out what is the equation of the least square regression line for predicting corn yield from the number of lamb’s quarter plants per meter.

(b)

Expert Solution
Check Mark

Answer to Problem 13E

  y^=a+bxy^=166.4831.0987x

Explanation of Solution

Now, as we know that in the question, the researcher examined the weeds among the corn yields and the computer output of this data is given. And also as we know the general regression equation be as:

  y^=a+bx

And the estimate a and b are given in the column of the computer output “Coef”:

  y^=a+bxy^=166.4831.0987x

with y^ the predicted corn yield and x the number of weeds per meter.

(c)

To determine

To interpret the slope and y -intercept of the regression line in this context.

(c)

Expert Solution
Check Mark

Explanation of Solution

Now, as we know that in the question, the researcher examined the weeds among the corn yields and the computer output of this data is given. And also as we know the general regression equation be as:

  y^=a+bx

And the estimate a and b are given in the column of the computer output “Coef”:

  y^=a+bxy^=166.4831.0987x

with y^ the predicted corn yield and x the number of weeds per meter.

Thus, the slope b is the coefficient of x and is thus 1.0987 . This means that the corn yield is expected to decrease by 1.0987 bushels per weed per meter.

And the y -intercept a is the constant of the regression equation and in thus 166.483 . This means that the cor yield is expected to be 166.483 when there are zero weeds per meter.

(d)

To determine

To explain do these data provide convincing evidence that more weeds reduce corn yield and carry out an appropriate test at the α=0.05 level.

(d)

Expert Solution
Check Mark

Answer to Problem 13E

Yes, there is sufficient evidence to support the claim that more weeds reduce corn yield.

Explanation of Solution

It is given in the computer output that:

  n=16b=1.0987SEb=0.5712

Thus, we define the hypothesis by:

  H0:β=0Ha:β<0

Thus, the value of the test statistics is as:

  t=bβSEb=1.098700.5712=1.923

And the degrees of freedom is:

  df=n2=162=14

Thus, the P-value is as:

  0.025<P<0.05

Or using technology the P-value is as:

  P=0.03753

As we know that if the P-value is less than or equal to the significance level, then the null hypothesis is rejected as:

  P<0.05 Reject H0

Thus, we conclude that there is sufficient evidence to support the claim that more weeds reduce corn yield.

Chapter 12 Solutions

The Practice of Statistics for AP - 4th Edition

Ch. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.2 - Prob. 1.1CYUCh. 12.2 - Prob. 1.2CYUCh. 12.2 - Prob. 1.3CYUCh. 12.2 - Prob. 1.4CYUCh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - Prob. 50ECh. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12 - Prob. 1CRECh. 12 - Prob. 2CRECh. 12 - Prob. 3CRECh. 12 - Prob. 4CRECh. 12 - Prob. 5CRECh. 12 - Prob. 6CRECh. 12 - Prob. 1PTCh. 12 - Prob. 2PTCh. 12 - Prob. 3PTCh. 12 - Prob. 4PTCh. 12 - Prob. 5PTCh. 12 - Prob. 6PTCh. 12 - Prob. 7PTCh. 12 - Prob. 8PTCh. 12 - Prob. 9PTCh. 12 - Prob. 10PTCh. 12 - Prob. 11PTCh. 12 - Prob. 12PTCh. 12 - Prob. 1PT4Ch. 12 - Prob. 2PT4Ch. 12 - Prob. 3PT4Ch. 12 - Prob. 4PT4Ch. 12 - Prob. 5PT4Ch. 12 - Prob. 6PT4Ch. 12 - Prob. 7PT4Ch. 12 - Prob. 8PT4Ch. 12 - Prob. 9PT4Ch. 12 - Prob. 10PT4Ch. 12 - Prob. 11PT4Ch. 12 - Prob. 12PT4Ch. 12 - Prob. 13PT4Ch. 12 - Prob. 14PT4Ch. 12 - Prob. 15PT4Ch. 12 - Prob. 16PT4Ch. 12 - Prob. 17PT4Ch. 12 - Prob. 18PT4Ch. 12 - Prob. 19PT4Ch. 12 - Prob. 20PT4Ch. 12 - Prob. 21PT4Ch. 12 - Prob. 22PT4Ch. 12 - Prob. 23PT4Ch. 12 - Prob. 24PT4Ch. 12 - Prob. 25PT4Ch. 12 - Prob. 26PT4Ch. 12 - Prob. 27PT4Ch. 12 - Prob. 28PT4Ch. 12 - Prob. 29PT4Ch. 12 - Prob. 30PT4Ch. 12 - Prob. 31PT4Ch. 12 - Prob. 32PT4Ch. 12 - Prob. 33PT4Ch. 12 - Prob. 34PT4Ch. 12 - Prob. 35PT4Ch. 12 - Prob. 36PT4Ch. 12 - Prob. 37PT4Ch. 12 - Prob. 38PT4Ch. 12 - Prob. 39PT4Ch. 12 - Prob. 40PT4Ch. 12 - Prob. 41PT4Ch. 12 - Prob. 42PT4Ch. 12 - Prob. 43PT4Ch. 12 - Prob. 44PT4Ch. 12 - Prob. 45PT4Ch. 12 - Prob. 46PT4
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