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?Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase wi

Statistics: Informed Decisions Using Data | 5th Edition | ISBN: 9780134133539 | Authors: Michael Sullivan III ISBN: 9780134133539 240

Solution for problem 2 Chapter 14

Statistics: Informed Decisions Using Data | 5th Edition

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Statistics: Informed Decisions Using Data | 5th Edition | ISBN: 9780134133539 | Authors: Michael Sullivan III

Statistics: Informed Decisions Using Data | 5th Edition

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14
1
Problem 2

Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following table lists the temperature (in degrees Fahrenheit, °F) and the number of chirps per second for the striped ground cricket.

(a) What are the estimates of b0 and b1? What is the mean number of chirps when the temperature is 80.2°F?

(b) Compute the standard error of the estimate, se. (c) Determine whether the residuals are normally distributed.

(d) Determine sb1

(e) If the residuals are normally distributed, test whether a linear relation exists between the explanatory variable, x, and response variable, y, at the a = 0.05 level of significance

f) If the residuals are normally distributed, construct a 95% confidence interval for the slope of the true leastsquares regression line.

(g) Construct a 90% confidence interval for the mean number of chirps found in part (a).

(h) Predict the number of chirps on a day when the temperature is 80.2°F.

(i) Construct a 90% prediction interval for the number of chirps found in part (h).

(j) Explain why the predicted number of chirps found in parts (a) and (h) are the same, yet the intervals are different.

Step-by-Step Solution:

Step 1 of 5) Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following table lists the temperature (in degrees Fahrenheit, °F) and the number of chirps per second for the striped ground cricket. (a) What are the estimates of b0 and b1 What is the mean number of chirps when the temperature is 80.2°F (b) Compute the standard error of the estimate, se. (c) Determine whether the residuals are normally distributed. (d) Determine sb1 (e) If the residuals are normally distributed, test whether a linear relation exists between the explanatory variable, x, and response variable, y, at the a = 0.05 level of significance f) If the residuals are normally distributed, construct a 95% confidence interval for the slope of the true leastsquares regression line. (g) Construct a 90% confidence interval for the mean number of chirps found in part (a). (h) Predict the number of chirps on a day when the temperature is 80.2°F. (i) Construct a 90% prediction interval for the number of chirps found in part (h). (j) Explain why the predicted number of chirps found in parts (a) and (h) are the same, yet the intervals are different.

Step 2 of 2

Chapter 14, Problem 2 is Solved
Textbook: Statistics: Informed Decisions Using Data
Edition: 5
Author: Michael Sullivan III
ISBN: 9780134133539

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?Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase wi