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ASSIGNMENT #3

IE 323 – Fall 2019

Due Date: Friday, 9/20 by noon Textbook: p. 302-303 53, 55, 59, 63, 67, 69

p. 334-335 1, 15, 17

1. TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streaming is gaining popularity. The Harris poll reported on November 13, 2012, that 1242 of 2343 American adults surveyed said they have watched digitally streamed TV programming on some type of device.

1. 1. Calculate a 99% confidence interval for the proportion of all adult Americans who watched streamed programming up to that point in time.

   2. What sample size would be required for the width of the interval to be within 0.015.

   3. What would be the maximum sample size needed for an error = 0.015 (disregarding the value of from part (a)?

   4. What do you think accounts for the small (or large) difference in sample sizes between parts (b) and (c)?

1. Two processes produce forgings used in an aircraft wing assembly. Of 200 forgings selected from process 1, 10 do not conform to the strength specifications, whereas of 300 forgings selected from process 2, 20 are nonconforming. Construct a 90% confidence interval on the difference in fraction nonconforming between the two processes. Can you say that the two processes are producing equal fraction nonconforming forgings?

1. A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with a standard deviation of 60. Let  denote the true average compressive strength.

1. What are the appropriate null and alternative hypotheses?

2. Consider a test procedure using for 20 randomly selected specimens. The rejection region is > 1331.26. Calculate the probability of committing a Type I error for the test and depict the error probability graphically.

3. Using the test procedure of part (b), what is the probability of committing a Type II error if  = 1350? Depict the Type I error from part (b) and the Type II error graphically.

1. A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph (under specified conditions) is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly suggests a reduction in the true average braking distance.

1. State the appropriate null and alternative hypotheses.

2. Suppose braking distance for the new system is normally distributed with  = 10. Let denote the sample average braking distance for a random sample of 36 observations. Calculate the Type I error probability for a critical region of < 115.20. Depict the Type I error probability graphically.

3. What is the probability that the new design is not implemented when its true average braking distance is actually 115 ft. and the critical region from part (b) is used? Depict the two error probabilities graphically.

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