A diet pill is given to 9 subjects over six weeks. The average difference in weight (follow up - baseline) is -2 pounds. What would the standard deviation have to be for the 95% T confidence interval to lie entirely below 0?
ANSWER: Around 2.6 pounds or less
Refer to the previous question. The interval would up being [-3.5, -0.5] pounds. What can be said about the population mean weight loss at 95% confidence?
A: We can not rule out the possibility of no mean weight loss at 95% confidence.
B: There is support of mean weight gain at 95% confidence.
C: There is support at 95% confidence of mean weight loss.
D: We can not rule out the possibility of mean weight gain at 95% confidence.
The Attempt at a Solution
I have three attempts to answer this question.
On my first attempt, I said D, thinking that since 5% of intervals do not contain the population mean, there is a chance that the population mean could be positive (and there a mean weight gain). But I got the wrong answer, and I don't understand why.
On my second attempt, I thought that "weight gain" wasn't necessarily going to occur but "no mean weight loss" was, so I chose A, and I still got the wrong answer.
I am surprised that confidence intervals will guarantee a support (as the remaining answers of the question suggest), so I now think the answer is C. B sounds ridiculous, because it doesn't make sense why there is support for mean weight gain at 95% confidence.
Can someone help me understanding the question? I hope I finally get this question right.