Ten different families were tested for the average number of litres of water they used per week before and after viewing a conservation video.A 95% confidence interval for the difference of the means after and before the training,μA - μB,was determined to be (-10.3,-4.1).
A)Based on this sample,we are 95% confident that the average decrease in weekly water consumption after viewing the conservation video is between 4.1 and 10.3 litres.
B)We are 95% confident that a randomly selected family who has viewed the video will use between 4.1 and 10.3 fewer litres of water per week compared to a randomly selected family who has not viewed the video.
C)We are 95% confident that a randomly selected family who has viewed the video will use between 4.1 and 10.3 more litres of water per week compared to a randomly selected family who has not viewed the video.
D)We know that 95% of families will use between 4.1 and 10.3 fewer litres of water each week after viewing the conservation video.
E)Based on this sample,we are 95% confident that the average increase in weekly water consumption after viewing the conservation video is between 4.1 and 10.3 litres.

Question

Quizplus · Accepted Answer

The confidence interval (-10.3,-4.1) means that we are 95% confident that the true difference between the means of the two groups (after and before the conservation video) falls within this interval, which means that we are 95% confident that the average decrease in weekly water consumption after viewing the video is between 4.1 and 10.3 litres. Option B is incorrect because we cannot generalize the sample to the entire population of families who may or may not have viewed the video. Option C is incorrect because the interval is for a decrease, not an increase. Option D is incorrect as we cannot make a statement about “95% of families” with confidence. Option E is incorrect because, as mentioned earlier, the interval is for a decrease, not an increase.

Ten Different Families Were Tested for the Average Number of Litres