Name:_____________________________________per.____ PSU Stat-Sect 7-4 Notes χ 2 Confidence Intervals
How many B days until the end of the semester?__________ The FINAL Exam:___________% of grade
PSU does a Plus and Minus Grade…A - = __________, B + = ________, B = _________, B - =_________
What is χ ?________________________ How does it relate to confidence intervals?_____________________
__________________________________________________________________________________________
When do we get a symmetric χ 2 curve?
Calculator Program:
:ClrHome
:Input “Area Right =”, T
:Input “DF=”, D
: “χ 2 cdf (X, 1E99, D) – T”  Y
0
:Disp solve ( Y
0
, X, 1.5*D, {0, 1E99} )
Example 1: Find the critical values for χ 2 right
and χ 2 left for a 90% confidence interval when n = 25.

Remember the difference between s and s 2

Example 2: Find the 95% confidence interval for the variance and standard deviation of the nicotine content of cigarettes manufactured if a sample of 20 cigarettes has a standard deviation of 1.6 milligrams.
Example 3:
GROUP Challenge: U.S. insurers’ costs for knee replacement surgery range from $17,627 to $25,462. Estimate the population variance (standard deviation) in cost with 98% confidence based on a random sample of 10 persons who have had this surgery. The retail costs (for uninsured persons) for the same procedure range from $40,640 to $58,702.
Estimate the population variance and standard deviation in cost with 98% confidence based on a sample.

Homework: Select the type of Confidence Interval you have in each Situation
Z-Score for Population T-Score for Sample Proportion or Chi-Squared
1. For a certain urban area, in a sample of 5 months, on average 28 mail carriers were bitten by dogs each month. The standard deviation of the sample was 3. Find the 90% confidence interval of the true mean number of mail carriers who are bitten by dogs each month. Assume the variable is normally distributed.
Z-Score for Population T-Score for Sample Proportion or Chi-Squared
2. In a study of 200 accidents that required treatment in an emergency room, 80 occurred at work. Find the 90% confidence interval of the true proportion of accidents that occurred at work.
Z-Score for Population T-Score for Sample Proportion or Chi-Squared
3. A U.S. Travel Data Center survey reported that Americans stayed an average of 7.5 nights when they went on vacation. The sample size was 1500.Find a point estimate of the population mean. Find the 95% confidence interval of the true mean. Assume the population standard deviation was 0.8.

Z-Score for Population T-Score for Sample Proportion or Chi-Squared
4. A random sample of 22 lawn mowers was selected, and the motors were tested to see how many miles per gallon of gasoline each one obtained. The variance of the measurements was 2.6. Find the 95% confidence interval of the true variance.
Z-Score for Population T-Score for Sample Proportion or Chi-Squared
5. Eight chemical elements do not have isotopes (different forms of the same element having the same atomic number but different atomic weights). A random sample of 30 of the elements that do have isotopes showed a mean number of
19.63 isotopes per element and the population a standard deviation of 18.73. Estimate the true mean number of isotopes for all elements with isotopes with 90% confidence.
Z-Score for Population T-Score for Sample Proportion or Chi-Squared
6. The standard deviation of the diameter of 18 baseballs was 0.29 cm. Find the 95% confidence interval of the true standard deviation of the diameters of the baseballs. Do you think the manufacturing process should be checked for inconsistency?