# Confidence interval for sample mean (possible error in text)

I am working through a problem on CI for a sample mean and I cannot get the answer listed in the text I have. I am wondering if I am missing something or whether the text may be incorrect.

We are given a sample of 10 scores:

45,38,52,48,25,39,51,46,55,46


I get a mean of 44.5 and SD of 8.68 which is the same as the solutions listed. I also get a standard error of the mean of 2.75 which is the same as the solutions.

However I cannot get the final answer. We are asked to calculate a 95% CI for the mean. When I calculate the margin of error (standard error of the mean * tcritical) I get the answer 2.75*2.262=6.2. (I choose df= 9). Thus the CI I get is 38.3 - 50.7.

However, the text says it is 28.35-60.65. Am I missing something? I would be really grateful for any comments. Thanks.

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I got the same confidence interval that you got. –  mark999 Jun 1 '11 at 7:17
It does look as if the text may have added 10 to the margin of error for the mean. Another, less likely, possibility is that the text is looking at the distribution of the population rather than the mean: 9 of the 10 values are inside the text's interval. –  Henry Jun 1 '11 at 15:24
@Mark999. Thank you. –  Anne Jun 1 '11 at 15:27
@Henry. Thank you. Can you say more about your second line, the possibility that it is looking at the distribution of the population? –  Anne Jun 1 '11 at 15:28
@Anne: The text's interval is very wide, so trying to guess the cause raises various possibilities: the fact that it contains almost all of the sample might suggest that it is based on the population distribution rather than the sample mean distribution, though I have not spotted a calculation which leads to its numbers. Alternatively, the text's interval is $44.5 \pm 16.15$ compared with your $44.5 \pm 6.2$; hence the possibility of a 10 creeping in. Both of these are speculation. –  Henry Jun 1 '11 at 15:43