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Seat Choice and GPAA biology professor wants to
Chapter 5, Problem 7RE(choose chapter or problem)
Seat Choice and GPA A biology professor wants to investigate the relation between the seat location chosen by a student on the first day of class and the student’s cumulative grade point average. He randomly selected an introductory biology class and obtained the following information for the 38 students in the class.
(a) Treating row as the explanatory variable, determine the estimates of \(\beta_0\) and \(\beta_1\). What is the mean GPA of students who choose a seat in the fifth row?
(b) Compute the standard error of the estimate, \(s_e\).
(c) Determine whether the residuals are normally distributed.
(d) If the residuals are normally distributed, determine \(s_{b_1}\).
(e) If the residuals are normally distributed, test whether a linear relation exists between the explanatory variable, row choice, and response variable, GPA, at the \(\alpha = 0.05\) level of significance.
(f) If the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares regression line.
(g) Construct a 95% confidence interval for the mean GPA of students who choose a seat in the fifth row.
(h) Predict the GPA of a randomly selected student who chooses a seat in the fifth row.
(i) Construct a 95% prediction interval for the GPA found in part (h).
(j) Explain why the predicted GPAs found in parts (a) and (h) are the same, yet the intervals are different.
Questions & Answers
QUESTION:
Seat Choice and GPA A biology professor wants to investigate the relation between the seat location chosen by a student on the first day of class and the student’s cumulative grade point average. He randomly selected an introductory biology class and obtained the following information for the 38 students in the class.
(a) Treating row as the explanatory variable, determine the estimates of \(\beta_0\) and \(\beta_1\). What is the mean GPA of students who choose a seat in the fifth row?
(b) Compute the standard error of the estimate, \(s_e\).
(c) Determine whether the residuals are normally distributed.
(d) If the residuals are normally distributed, determine \(s_{b_1}\).
(e) If the residuals are normally distributed, test whether a linear relation exists between the explanatory variable, row choice, and response variable, GPA, at the \(\alpha = 0.05\) level of significance.
(f) If the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares regression line.
(g) Construct a 95% confidence interval for the mean GPA of students who choose a seat in the fifth row.
(h) Predict the GPA of a randomly selected student who chooses a seat in the fifth row.
(i) Construct a 95% prediction interval for the GPA found in part (h).
(j) Explain why the predicted GPAs found in parts (a) and (h) are the same, yet the intervals are different.
ANSWER:Step 1 of 11
(a) Treating row as the explanatory variable, determine the estimates of ?0 and ?1. What is the mean GPA of students who choose a seat in the fifth row?