Chapter 10 Confidence Intervals

Your test on Chapter 10 will be Tuesday, February 17.
HW due Friday: Either problem 10.53 worked out in detail showing all work or problems 10.54 and 10.58 worked cout completely.
Have you hugged your study guide lately????
HW due Thursday: Problems 10.38 and .44. 1st and 2nd periods, please bring all HW from this week on Thursday.

Today we computed paired t confidence intervals for the difference in grip strength between right and left hands.

You can find the t* value for any number of df by using the calculator;
STAT TESTS T-INT Stats x-bar = 0, sx = sqrt df+1, n = df+1, conf level = whatever you need, like .95.

ALL students should have finished 10.28, 10.30, 10.31, and 10.31 PLUS the summary of the cautions. Have these with you on Wednesday.

HW for 1st and 2nd periods: Summarize the cautions of section 10.1 (pages 635-637) in your own words and work problems 10.28 and 10.30.
Periods 6 & 7: Work problems 10.7-10.10 PLUS summarize the cautions above.

The question was raised: Why do we use 2 sometimes and 1.96 other times for Z*? As you probably recall, approximately 95% of the data in a Normal distribution will fall within about 2 standard deviations of the mean, but that was just an estimate. The more precise number of standard deviations that form the 95% boundaries is 1.96. Use that whenever we are using Z procedures UNLESS we are just looking for a quick and dirty estimate. but NOT when we are constructing confidence intervals.

When do we use sx and when do we use sigmax? Sigma represents the population standard deviation, a number we rarely know. On the other hand, sx represents our sample standard deviation. When we do not know the population standard deviation we will use t procedures instead of z procedures.

And, of course, we divide by sqrt of n to convert these standard deviations into standard errors of x-bar.



Some web-based applets for Confidence Intervals: Rice Univ Freeman

HW due Friday--
1st and 2nd per: Problems 10.7-10.10 from the text. You should have already worked the problems from the REVIEW III on pages 610 and 611.
6th and 7th per: "Review III" questions following Chapter 9 on pages 610-611 in the text AND print one page from a confidence interval applet from the web and be able to explain it.

Key concepts from today: Approximately 95% of sample averages will fall within about 2 std dev/Sqrt(n) of the population mean. If we don't know what the population mean is, we might reason that our point estimate (x-bar) is a pretty good guess, and that 95% of the time, our sample averages will fall within 2 std dev/sqrt(n) of the true mean. Then the interval (x-bar minus 2*std dev/sqrt(n), x-bar plus 2*std dev/sqrt(n)) is our confidence interval or reasonable guess at the value of the population mean. About 95% of these intervals will capture the true mean. The distance from the mean to the upper bound (or event the lower bound) is the margin of error.

These are NOT true: 95% of the time this interval contains the mean. 95% of population means fall inside this interval. 95% of the time the mean falls between lower bound and upper bound. NONE of these are true, so DO NOT write these as interpretations of the confidence intervals.

Instead, we are 95% confident that the mean falls between the lower bound and the upper bound.

If you did not work problems from the review following Chapter 9, now is the time!!!!