Suppose you work for a large contracting company, and are responsible for managing the supply of paint at your storehouse, which is restocked weekly. You record the amount of paint left over at the end of the week. You wish to create a regression model to predict the amount of cans of paint that will be left over at the end of the day, using the planned number of hours of painting to be done in the week. After analyzing the past 28 weeks of inventory, you create the following regression model: ŷ = 56.4-0.69x, where is the number of hours spent painting that week and ŷ is the predicted ending inventory level in cans of paint. Your analysis also yielded a SE(b₁) of 0.51. Using this information, construct a confidence interval around the regression slope of your analysis, with a 95% confidence level. Using this information, select the correct statements about of your analysis with respect to the test below. When necessary, round your answers to three decimal places. (select all choices that apply). [H₁: B₁ = 0 HA: 0₁ 0 The upper limit of the confidence interval around the regression slope is approximately 0.359. The null hypothesis is rejected, since the upper and the lower limits of the confidence interval are strictly greater than zero. The margin of error for the confidence interval around the regression slope is approximately 1.049. The null hypothesis is rejected, since the upper and lower limits of the confidence interval around the regression slope are strictly less than zero. The null hypothesis cannot be rejected, since the confidence interval around the regression slope contains zero. The lower limit of the confidence interval around the regression slope is approximately -1.657.
Suppose you work for a large contracting company, and are responsible for managing the supply of paint at your storehouse, which is restocked weekly. You record the amount of paint left over at the end of the week. You wish to create a regression model to predict the amount of cans of paint that will be left over at the end of the day, using the planned number of hours of painting to be done in the week. After analyzing the past 28 weeks of inventory, you create the following regression model: ŷ = 56.4-0.69x, where is the number of hours spent painting that week and ŷ is the predicted ending inventory level in cans of paint. Your analysis also yielded a SE(b₁) of 0.51. Using this information, construct a confidence interval around the regression slope of your analysis, with a 95% confidence level. Using this information, select the correct statements about of your analysis with respect to the test below. When necessary, round your answers to three decimal places. (select all choices that apply). [H₁: B₁ = 0 HA: 0₁ 0 The upper limit of the confidence interval around the regression slope is approximately 0.359. The null hypothesis is rejected, since the upper and the lower limits of the confidence interval are strictly greater than zero. The margin of error for the confidence interval around the regression slope is approximately 1.049. The null hypothesis is rejected, since the upper and lower limits of the confidence interval around the regression slope are strictly less than zero. The null hypothesis cannot be rejected, since the confidence interval around the regression slope contains zero. The lower limit of the confidence interval around the regression slope is approximately -1.657.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 2SGR
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Transcribed Image Text:Suppose you work for a large contracting company, and are responsible for managing
the supply of paint at your storehouse, which is restocked weekly. You record the
amount of paint left over at the end of the week. You wish to create a regression
model to predict the amount of cans of paint that will be left over at the end of the
day, using the planned number of hours of painting to be done in the week. After
analyzing the past 28 weeks of inventory, you create the following regression model:
ŷ 56.4 0.69x,
=
where x is the number of hours spent painting that week and ŷ is the predicted
ending inventory level in cans of paint. Your analysis also yielded a SE(b₁) of 0.51.
Using this information, construct a confidence interval around the regression slope
of your analysis, with a 95% confidence level. Using this information, select the
correct statements about of your analysis with respect to the test below. When
necessary, round your answers to three decimal places. (select all choices that apply).
Ho: : B₁ = 0
HA: B₁0
The upper limit of the confidence interval around the regression slope is
approximately 0.359.
The null hypothesis is rejected, since the upper and the lower limits of the
confidence interval are strictly greater than zero.
The margin of error for the confidence interval around the regression slope is
approximately 1.049.
The null hypothesis is rejected, since the upper and lower limits of the
confidence interval around the regression slope are strictly less than zero.
The null hypothesis cannot be rejected, since the confidence interval around the
regression slope contains zero.
The lower limit of the confidence interval around the regression slope is
approximately -1.657.
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