Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.stat.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Understanding Confidence Intervals. Please comment.
Replies:
1
Last Post:
Nov 9, 2009 3:20 PM



Bacle
Posts:
818
From:
NYC
Registered:
6/21/09


Understanding Confidence Intervals. Please comment.
Posted:
Nov 9, 2009 2:30 AM


Could someone please tell me if I am understanding confidence intervals correctly.?. Here is a problem I am trying to answer.( I will mark my answers with a  to make it easier to recognize. Please feel free to check just oneortwo of the answers if this seems too long). I would appreciate your comments:
Here is the problem:
Teachers Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What's wrong with the others?
tInterval for m: with 90.00% Confidence, 38944 < m(TchPay) < 42893
a)If we took many random samples of Nevada teachers, about 9 out of 10 of them would produce this confidence interval.
 a)False: the confidence interval would depend on the value of sampling mean. Since we are using tintervals, we must be using the sample error, which makes intervals even more variable than if we knew the true pop. standard deviation.
All we can say is that there is a 95% probability that the true average salary lies in a 95% confidence interval, whatever interval we construct.
________________________________________________
b)If we took many random samples of Nevada teachers, about 9 out of 10 of them would produce a confidence interval that contained the mean salary of all Nevada teachers.
 True, if we constructed 95% confidence tintervals with the sampling data given.
____________________________________________________
c)About 9 out of 10 Nevada teachers earn between $38,944 and $42,893.

False. The confidence interval is about the true population mean, about the probability that the true mean lies in the interval, not about the probability that a teacher earns an amount in this range.
_________________________________________________________
d)About 9 out of 10 of the teachers surveyed earn between $38,944 and $42,893. 
False.
_____________________________________________________
d)We are 90% confident that the average teacher salary in the United States is between $38,944 and $42,893.

d)True. This is the actual meaning of a confidence interval.
Thanks For Any Comments.



