# Confidence interval and 6 degrees of freedom

See attached data file.

#1.

8.15:

Using Table A.4 (page 640), find t.100, t.025, and t.001 based on 11 degrees of freedom. Also, find these t points based on 6 degrees of freedom.

#2.

8.16:

Suppose that for a sample of n = 11 measurements, we find that _ = 72 and s 5. Assuming normality, compute confidence intervals for the population mean ? with the following levels of confidence: x¯

a: 95%

b: 99%

c: 80%

d: 90%

e: 98%

f: 99.8%

#3.

8.17:

The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose a random sample of seven Ohio banks is selected and that the bad debt ratios (written as percentages) for these banks are 7 percent, 4 percent, 6 percent, 7 percent, 5 percent, 4 percent, and 9 percent. Assuming the bad debt ratios are approximately normally distributed, the MINITAB output of a 95 percent confidence interval for the mean bad debt ratio of all Ohio banks is as follows:

Variance: D-Ratio

N: 7

Mean: 6.00000

St. Dev: 1.82574

SE Mean: 0.69007

95% CI: (4.31147, 7.68853)

A: Using the Xbar and s on the MINITAB output, verify the calculation of the 95 percent confidence interval, and calculate a 99 percent confidence interval for the mean debt-to-equity ratio.

#4.

8.19

Air traffic controllers have the crucial task of ensuring that aircraft don't collide. To do this, they must quickly discern when two planes are about to enter the same air space at the same time. They are aided by video display panels that track the aircraft in their sector and alert the controller when two flight paths are about to converge. The display panel currently in use has a mean "alert time" of 15 seconds. (The alert time is the time elapsing between the instant when two aircraft enter into a collision course and when a controller initiates a call to reroute the planes.) According to Ralph Rudd, a supervisor of air traffic controllers at the Greater Cincinnati International Airport, a new display panel has been developed that uses artificial intelligence to project a plane's current flight path into the future. This new panel provides air traffic controllers with an earlier warning that a collision is likely. It is hoped that the mean "alert time," ?, for the new panel is less than 8 seconds. In order to test the new panel, 15 randomly selected air traffic controllers are trained to use the panel and their alert times for a simulated collision course are recorded. The sample alert times (in seconds) are: 7.2, 7.5, 8.0, 6.8, 7.2, 8.4, 5.3, 7.3, 7.6, 7.1, 9.4, 6.4, 7.9, 6.2, 8.7.

A: Using the fact that _ = 7.4 and s = 1.026, find a 95 percent confidence interval for the population mean alert time, ?, for the new panel.

#5.

8.21: A production supervisor at a major chemical company wishes to determine whether a new catalyst, catalyst XA-100, increases the mean hourly yield of a chemical process beyond the current mean hourly yield, which is known to be roughly equal to, but no more than, 750 pounds per hour. To test the new catalyst, five trial runs using catalyst XA-100 are made. The resulting yields for the trial runs (in pounds per hour) are 801, 814, 784, 836, and 820. Assuming that all factors affecting yields of the process have been held as constant as possible during the test runs, it is reasonable to regard the five yields obtained using the new catalyst as a random sample from the population of all possible yields that would be obtained by using the new catalyst. Furthermore, we will assume that this population is approximately normally distributed.

A: Using the Excel output in Figure 8.13, find a 95 percent confidence interval for the mean of all possible yields obtained using catalyst XA-100.

#### Solution Summary

Answers of multiple choice questions on confidence interval and control charts