Applied Statistics and Probability for Engineers 6th Edition solutions

Applied Statistics and Probability for Engineers 6
State whether each of the following situations is a correctly stated hypothesis testing problem and why. (a) \(H_0:\ \mu=25,\ H_1:\ \mu\ne25\) (b) \(H_0:\ \sigma>10,\ H_1:\ \sigma=10\) (c) \(H_{0}: \bar{x}=50, H_{1}: \bar{x} \neq 50\) (d) \(H_0:\ p=0.1,\ H_1:\ p=0.5\) (e) \(H_0:\ s=30,\ H_1

Applied Statistics and Probability for Engineers 6
A semiconductor manufacturer collects data from a new tool and conducts a hypothesis test with the null hypothesis that a critical dimension mean width equals 100 nm. The conclusion is to not reject the null hypothesis. Does this result provide strong evidence that the critical dimension mean equals

Applied Statistics and Probability for Engineers 6
The standard deviation of critical dimension thickness in semiconductor manufacturing is (a) State the null and alternative hypotheses used to demonstrate that the standard deviation is reduced. (b) Assume that the previous test does not reject the null hypothesis. Does this result provide strong

Applied Statistics and Probability for Engineers 6
The mean pull-off force of a connector depends on cure time. (a) State the null and alternative hypotheses used to demonstrate that the pull-off force is below 25 newtons. (b) Assume that the previous test does not reject the null hypothesis. Does this result provide strong evidence that the pull-off

Applied Statistics and Probability for Engineers 6
A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kil-ograms. The company wishes to test the hypothesis \(H_0:\ \mu=12\) against \(H_1:\ \mu<12\), using a random sample of four spec

Applied Statistics and Probability for Engineers 6
Repeat Exercise 9-5 using a sample size of n = 16 and the same critical region. Equation Transcription: Text Transcription: n=16

Applied Statistics and Probability for Engineers 6
In Exercise 9-5, find the boundary of the critical region if the type I error probability is (a) \(\alpha=0.01\) and \(n=4\) (c) \(\alpha=0.01\) and \(n=16\) (b) \(\alpha=0.05\) and \(n=4\) (d) \(\alpha=0.05\) and \(n=16\) Equation Transcription: Text Tran

Applied Statistics and Probability for Engineers 6
In Exercise 9-5, calculate the probability of a type II error if the true mean elongation is 11.5 kilograms and (a) \(\alpha=0.05\) and \(n=4\) (b) \(\alpha=0.05\) and \(n=16\) (c) Compare the values of \(\beta\) calculated in the previous parts. What conclusion can you draw?

Applied Statistics and Probability for Engineers 6
In Exercise 9-5, calculate the P-value if the observed statistic is (a) \(\bar{x}=11.25\) (b) \(\bar{x}=11.0\) (c) \(\bar{x}=11.75\) Equation Transcription: Text Transcription: x bar=11.25 x bar=11.0 x bar=11.75

Applied Statistics and Probability for Engineers 6
The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 100, and the standard deviation is 2. You wish to test \(H_0:\ \mu=100\) versus \(H_1:\ \mu\ne100\) with a sample of \(n=9\) specimens. (a) If the acceptance region is defined

Applied Statistics and Probability for Engineers 6
Repeat Exercise 9-10 using a sample size of \(n=5\) and the same acceptance region. Equation Transcription: Text Transcription: n=5

Applied Statistics and Probability for Engineers 6
In Exercise 9-10, find the boundary of the critical region if the type I error probability is (a) \(\alpha=0.01\) and \(n=9\) (c) \(\alpha=0.01\) and \(n=5\) (b) \(\alpha=0.05\) and \(n=9\) (d) \(\alpha=0.05\) and \(n=5\) Equation Transcription:

Applied Statistics and Probability for Engineers 6
In Exercise 9-10, calculate the probability of a type II error if the true mean heat evolved is 103 and (a) \(\alpha=0.05\) and \(n=9\) (b) \(\alpha=0.05\) and \(n=5\) (c) Compare the values of \(\beta\) calculated in the previous parts. What conclusion can you draw? Equa

Applied Statistics and Probability for Engineers 6
In Exercise 9-10, calculate the P-value if the observed statistic is (a) \(\bar{x}=98\) (b) \(\bar{x}=101\) (c) \(\bar{x}=102\) Equation Transcription: Text Transcription: x bar=98 x bar=101 x bar=102

Applied Statistics and Probability for Engineers 6
A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test \(H_0:\ \mu=175\) millimeters versus \(H_1:\ \mu>175\) millimeters,

Applied Statistics and Probability for Engineers 6
Repeat Exercise 9-15 assuming that the sample size is \(n=16\) and the boundary of the critical region is the same. Equation Transcription: Text Transcription: n=16

Applied Statistics and Probability for Engineers 6
In Exercise 9-15, find the boundary of the critical region if the type I error probability is (a) \(\alpha=0.01\) and \(n=10\) (c) \(\alpha=0.01\) and \(n=16\) (b) \(\alpha=0.05\) and \(n=10\) (d) \(\alpha=0.05\) and \(n=16\) Equation Trans

Applied Statistics and Probability for Engineers 6
In Exercise 9-15, calculate the probability of a type II error if the true mean foam height is 185 millimeters and (a) \(\alpha=0.05\) and \(n=10\) (b) \(\alpha=0.05\) and \(n=16\) (c) Compare the values of \(\beta\) calculated in the previous parts. What conclusion can you draw?

Applied Statistics and Probability for Engineers 6
In Exercise 9-15, calculate the P-value if the observed statistic is (a) \(\bar{x}=180\) (b) \(\bar{x}=190\) (c) \(\bar{x}=170\) Equation Transcription: Text Transcription: x bar=180 x bar=190 x bar=170

Applied Statistics and Probability for Engineers 6
A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed with standard deviation 0.25 volt, and the manufacturer wishes to test \(H_0:\ \mu=5\) volts against \(H_1:\ \mu\ne5\) volts, using \(n=8\) units. (a) The acceptan

Applied Statistics and Probability for Engineers 6
Rework Exercise 9-20 when the sample size is 16 and the boundaries of the acceptance region do not change. What impact does the change in sample size have on the results of parts (a) and (b)?

Applied Statistics and Probability for Engineers 6
In Exercise 9-20, find the boundary of the critical region if the type I error probability is (a) \(\alpha=0.01\) and \(n=8\) (c) \(\alpha=0.01\) and \(n=16\) (b) \(\alpha=0.05\) and \(n=8\) (d) \(\alpha=0.05\) and \(n=16\) Equation Transcription:

Applied Statistics and Probability for Engineers 6
In Exercise 9-20, calculate the P-value if the observed statistic is (a) \(\bar{x}=5.2\) (b) \(\bar{x}=4.7\) (c) \(\bar{x}=5.1\)

Applied Statistics and Probability for Engineers 6
In Exercise 9-20, calculate the probability of a type II error if the true mean output is 5.05 volts and (a) \(\alpha=0.05\) and \(n=10\) (b) \(\alpha=0.05\) and \(n=16\) (c) Compare the values of \(\beta\) calculated in the previous parts. What conclusion can you draw?

Applied Statistics and Probability for Engineers 6
Problem 25E The proportion of adults living in Tempe, Arizona, who are college graduates is estimated to be p = 0.4. To test this hypothesis, a random sample of 15 Tempe adults is selected. If the number of college graduates is between 4 and 8, the hypothesis will be accepted; otherwise, you will con

Applied Statistics and Probability for Engineers 6
The proportion of residents in Phoenix favoring the building of toll roads to complete the freeway system is believed to be p = 0.3. If a random sample of 10 residents shows that 1 or fewer favor this proposal, we will conclude that p < 0.3. (a) Find the probability of type I error if the true propor

Applied Statistics and Probability for Engineers 6
A random sample of 500 registered voters in Phoenix is asked whether they favor the use of oxygenated fuels year-round to reduce air pollution. If more than 400 voters respond positively, we will conclude that more than 60% of the voters favor the use of these fuels. (a) Find the probability of type

Applied Statistics and Probability for Engineers 6
If we plot the probability of accepting \(H_0:\ \mu=\mu_0\) versus various values of \(\mu\) and connect the points with a smooth curve, we obtain the operating characteristic curve (or the OC curve) of the test procedure. These curves are used extensively in industrial applications of hypothesis

Applied Statistics and Probability for Engineers 6
Problem 29E A quality-control inspector is testing a batch of printed circuit boards to see whether they are capable of performing in a high temperature environment. He knows that the boards that will survive will pass all five of the tests with probability 98%. They will pass at least four tests wit