Questions on engineering statistics

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ISE 320 Engineering Statistics

Homework 1

1. To answer this homework, you take quiz in WebCT. It’s name is “ HW 1”. You should submit the quiz by Wednesday 24 Sept at 2 PM.

2. Only the finalanswer should be entered in the answer box. DONOT show the steps.The computer will be used to grade your work so do not write any comments or explanations.

3. The data of each question is given a name as shown below in red color. Each student has his own data.The data is in the file: HW 1 Data.xlsx. Your data is written next to your name for each question.Erase the data of the other students so you don’t use their data.

Thank you and good luck

Questions on Chapter 7

Question 1:

X is a random variable with mean a and variance b. Y is another random variable with mean c and standard deviationd. X and Y are independent. Then the E(mX – nY) = , Var(mX – nY) =

Question 2: Use 3 decimal places

A machine produces shafts with random diameter that follows a normal distribution with mean and variance as those of the random variable X in Question 1. A random sample of n shafts is selected. Let be the sample average. The distribution of = , the mean of = and the variance of =

Questions on Chapter 8

Question 3:Use 4 decimal places

A machine produces shafts with random diameter that follows a normal distribution with variance b. A random sample is taken. The sample readings are in the data file. The two sided (1-α)% confidence interval of the mean =

≤ µ ≤

Question 4:Use 4 decimal places

Using the same readingsand the same αof Question 3, the lower side confidence interval on the mean =

≤ µ ≤

Question 5: Use 7 decimal places in the calculations but show the final answer in 3 decimal places

Using the same readings and the same αof Question 3, but the variance is unknown, the two sidedCI on the mean =

≤ µ ≤

Question 6: Use 7 decimal places in the calculations but show the final answer in 3 decimal places

Using the same readings and the same α of Question 3; the two sidedCI on the variance =

≤ σ2 ≤

Using the interval you generated, with confidence 1- α; write 1 if you think σ ≥ 1, write 2 if you think σ ≤ 1 and write 0 if you think that no conclusion can be made =

Question 7: Use 7 decimal places in the calculations but show the final answer in 3 decimal places

A machine produces shafts with random diameter. A random sample of is selected. The readings are in the data sheet. A shaft is considered defective if its diameter is less than e.Using the same αas in Question 3, the two sided CI of the proportion of defective shafts =

≤ P ≤

Questions on Chapter 10

Question 8:Use 7 decimal places in the calculations but show the final answer in 3 decimal places

Machine A produces shafts with random diameter that follows a normal distribution. The sample readings are the same as in Question 3. Machine B produces shafts with random diameter that follows a normal distribution with variance g. A random sample is selected. The readings of this sample are in the data file.Using the same α as in Question 3; the two sided CI on the difference of the means =

≤ µA - µB ≤

Using the interval you generated, with confidence 1- α; write 1 if you think µA≥ µB, write 2 if you think µA≤ µB and write 0 if you think that no conclusion can be made =

Question 9: Use 7 decimal places in the calculations but show the final answer in 3 decimal places

Solve the problem described in Question 8, however the variances are unknownand we believe that they are equal. The two sided CIon the difference of the means =

≤ µA - µB ≤

Question 10: Use 7 decimal places in the calculations but show the final answer in 3 decimal places

Solve the problem described in Question 8, however the variances are unknown and we believe that they different. The two sided CIon the difference of the means =

≤ µA - µB ≤

Question 11: Use 7 decimal places in the calculations but show the final answer in 3 decimal places

Consider the data and α of Question 8, the lower sided CI on the ratio of the variances =

Using the interval you generated, with confidence 1- α; write 1 if you think σA≥ σB, write 2 if you think σA≤ σB and write 0 if you think that no conclusion can be made =