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STAT 285 Assignment 2
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1. Each of the following is a confidence interval for

μ= true average (i.e. population mean) resonance

frequency (Hz) for all tennis rackets of a certain type: (114.4, 115.6), (114.1, 115.9).

(a) What is the value of the sample mean resonance frequency?

(b) Both intervals were calculated from the same sample data. The confidence level for one of these intervals is 90% and for the other is 99%. Which of the intervals has the 90% confidence level, and why?

2. A confidence interval for the true average stray-load loss

μ(watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with σ= 30

.

(a) Compute a 95% CI for μ when = 25 and x bar= 58.3

.

(b) Compute a 95% CI for μ when n= 100 and x bar = 58.3

.

(c) Compute a 99% CI for μ when n= 100 and x bar = 58.3

.

(d) Compute a 82% CI for μ when n= 100 and x= 58.3

3

.

(e) How large must n be if the width of the 99% interval for μ is to be 1.0?

3. The article “Ultimate Load Capacities of Expansion Anchor Bolts" (J. of Energy Engr., 1993: 139-

158) gave the following summary data on shear strength (kip) for a sample of 3/8-in. anchor bolts:

n= 78 x bar = 4.25  ,s= 1.

30

Calculate a lower confidence bound using a confidence level of 90% for true

average shear strength.

4. Determine the values of the following quantities: (a)χ20.1,15, (b)χ20.1,25, (c)χ20.01,25.

5. A triathlon consisting of swimming, cycling, and running is one of the more strenuous amateur sport-

ing events. The article “Cardiovascular and Thermal Response of Triathlon Performance" (

Medicine

and Science in Sports and Exercise, 1988: 385-389

) reports on a research study involving nine male

triathletes. Maximum heart rate (beats/min) was recorded during performance of each of the three

events. For swimming, the sample mean and sample standard deviation were 188.0 and 7.2, respec-

tively. Assuming that the heart rate distribution is (approximately) normal, construct a 98% CI for

true mean heart rate of triathletes while swimming.

6. A journal article reports that a sample of size 5 was used as a basis for calculating a 95% CI for the

true average natural frequency (Hz) of delaminated beams of a certain type. The resulting interval

was (229.764, 233.504). You decide that a confidence level of 99% is more appropriate than the 95%

level used. What are the limits of the 99% interval? [Hint: Use the center of the interval and its width

to determinē xands.

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STAT 285 Assignment 2
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