Question 977550: The following data show the number of hours studied for an exam, x, and the grade received on the exam, y (y is measured in 10's; that is, y = 8 means that the grade, rounded to the nearest 10 points, is 80).
x 2 3 3 3 3 4 4 5 5 6 6 7 8 8 8
y 5 5 6 7 8 7 9 7 8 7 9 10 8 9 10
Using the estimated standard error of regression, sb1 = 0.1435, for the number of hours studied–exam grade relationship, find the 95% confidence interval for the population slope β1. The equation for the line of best fit was y = 4.83 + 0.57x. (Give your answers correct to three decimal places.)
lower limit:
upper limit:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! y = 4.83 + 0.57x has the slope 0.57. This is the estimate of the population slope β1. Let's call m the estimate of the population slope.
n = 15
df = n-1 = 14
Critical Value (95% confidence, df = 14). Use this table
t = 2.145
Margin of Error (ME)
ME = t*Sb1 = 2.145*0.1435 = 0.3078075
ME = 0.3078075
Lower Bound (L)
L = m - ME
L = 0.57 - 0.3078075
L = 0.2621925
L = 0.262
Upper Bound (U)
U = m + ME
U = 0.57 + 0.3078075
U = 0.8778075
U = 0.878
Summary:
lower limit: 0.262
upper limit: 0.878
The 95% confidence interval for the slope β1 is (0.262, 0.878)
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