Question

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, was determined to be (−10.8,−4.2)

a. 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.
b. 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.
c. 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.
d. 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.
e. 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.

Answer 1

a. 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.

Explanation:

From the given information:

we learnt that :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, was determined to be (−10.8,−4.2)

Confidence interval shows the range of values with the likelihood to contain a true population value with a certain degree of confidence. In confidence interval, a true population mean lies within the interval of a lower limit and upper limit.

From the given information; the lower limit is -10.8 and the upper limit is -4.82; based on this negative sign, it means they are both decreasing.

Therefore; we can conclude from the given option that :

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.