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Stat 412 Assignment #4 Do all problems. Due: Wednesday, February 12, 2020 1. A semiconductor manufacturer collected data from a new tool and conducted a hypothesis test with the null hypothesis being a critical dimension mean width equals 100 nm. After the test was carried out, the conclusion was to reject the null hypothesis. Does the test provide strong evidence that the critical dimension mean width equals 100 nm? Explain your answer. 2. The true mean pull-off force of a connector depends upon the cure time. (a) State the null and alternative hypotheses that might be used to demonstrate that the pull-off force is below 25 Newtons. (b) Assume that the test in (a) does not reject the null hypothesis. Does it provide strong evidence that the pull-off force is greater than or equal to 25 newtons? Explain your answer. 3. The heat evolved in calories per gram of a cement mixture is found to follow distribution with standard deviation 2. The cement mixture will be used for a construction project unless evidence suggests that the true mean heat of the mixture is above 100. (a) Suppose mean heat based on a sample of size 25 is found to be 100.5. Formulate the appropriate hypotheses and then conclude if the cement mixture can be used for the project. Use ? = 0.05 (b) State the type of error that might have been committed in your conclusion in (a). 4. The tensile strength of a steel alloy intended for use in golf club shafts is known to be normally distributed with standard deviation of 60 psi. Suppose a random sample of 12 specimens has a mean tensile strength of 3450 psi. Is there evidence in data to conclude that the true mean strength differs from 3500 psi and draw your conclusions. Use ? = 0.10 5. A bearing used in an automotive application should have an inside diameter that does not differ from 1.5 inches. A random sample of 32 bearings is selected and the average inside diameter of these bearings is 1.4975 inches. You may assume that the bearing diameter is normally distributed and the standard deviation is 0.01 inches. On the basis of the sample information, can you conclude that the true mean diameter of bearings does not meet the required specification? 6. A random sample of 50 batteries is selected and subjected to a life test. The average life of these 50 batteries is 4.05 hours. Assume battery life is normally distributed with standard deviation 0.2 hours. Is there evidence in the data to support the claim that mean battery life exceeds 4 hours? Use ? = 0.02

Stat 412
Assignment #4
Do all problems. Due: Wednesday, February 12, 2020
1. A semiconductor manufacturer collected data from a new tool and conducted a hypothesis test with the null hypothesis being a critical dimension mean width equals 100 nm. After the test was carried out, the conclusion was to reject the null hypothesis. Does the test provide strong evidence that the critical dimension mean width equals 100 nm? Explain your answer.
2. The true mean pull-off force of a connector depends upon the cure time.
(a) State the null and alternative hypotheses that might be used to demonstrate that the pull-off force is below 25 Newtons.
(b) Assume that the test in (a) does not reject the null hypothesis. Does it provide strong evidence that the pull-off force is greater than or equal to 25 newtons? Explain your answer.
3. The heat evolved in calories per gram of a cement mixture is found to follow distribution with standard deviation 2. The cement mixture will be used for a construction project unless evidence suggests that the true mean heat of the mixture is above 100.
(a) Suppose mean heat based on a sample of size 25 is found to be 100.5. Formulate the appropriate hypotheses and then conclude if the cement mixture can be used for the project. Use ? = 0.05
(b) State the type of error that might have been committed in your conclusion in (a).
4. The tensile strength of a steel alloy intended for use in golf club shafts is known to be normally distributed with standard deviation of 60 psi. Suppose a random sample of 12 specimens has a mean tensile strength of 3450 psi. Is there evidence in data to conclude that the true mean strength differs from 3500 psi and draw your conclusions. Use ? = 0.10
5. A bearing used in an automotive application should have an inside diameter that does not differ from 1.5 inches. A random sample of 32 bearings is selected and the average inside diameter of these bearings is 1.4975 inches. You may assume that the bearing diameter is normally distributed and the standard deviation is 0.01 inches. On the basis of the sample information, can you conclude that the true mean diameter of bearings does not meet the required specification?
6. A random sample of 50 batteries is selected and subjected to a life test. The average life of these 50 batteries is 4.05 hours. Assume battery life is normally distributed with standard deviation 0.2 hours. Is there evidence in the data to support the claim that mean battery life exceeds 4 hours? Use ? = 0.02

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