Ten Different Families Were Tested for the Average Number of Gallons

question 14

Multiple Choice

Ten different families were tested for the average number of gallons of water they used per day before and after viewing a conservation video. A $90 \%$ confidence interval for the difference of the means after and before the training, $\mu _ { A } - \mu _ { B }$ was determined to be $( - 10.8 , - 4.2 )$ .

• A) We know that \(90 \%\) of families will use between \(4.2\) and \(10.8\) fewer gallons of water each day after viewing the conservation video.
• B) Based on this sample, we are \(90 \%\) confident that the average decrease in daily water consumption after viewing the conservation video is between \(4.2\) and \(10.8\) gallons.
• C) We are \(90 \%\) confident that a randomly selected family who has viewed the video will use between \(4.2\) and \(10.8\) more gallons of water per day compared to a randomly selected family who has not viewed the video.
• D) Based on this sample, we are \(90 \%\) confident that the average increase in daily water consumption after viewing the conservation video is between \(4.2\) and \(10.8\) gallons.
• E) We are \(90 \%\) confident that a randomly selected family who has viewed the video will use between \(4.2\) and \(10.8\) fewer gallons of water per day compared to a randomly selected family who has not viewed the video.

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Definitions:

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The amount of money for which a product or service is sold to customers.

Least-Squares Regression

A statistical method used to determine the line of best fit by minimizing the sum of squares of the differences between observed and predicted values.

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The squares of the differences between individual observations and the mean of those observations, often used in statistical analysis to measure variance.

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A statistical tool used in linear regression analysis that represents the relationship between two variables, showing the expected value of the dependent variable for a given value of the independent variable.