Answers to CRE questions in June 2019 Newsletter

1. Consider the regression results from the regression of Y against X for 50 observations:Y = 5.0 – 1.5 X

The standard error of the estimate is 0.40 and the standard error of the coefficient is 0.45.

The predicted value of Y if X is 10 is:

**a.-10**

b. 4.5

c. 10

d. 20

2. Which of the following is an assumption of linear regression? The:

a. expected value of the residuals is zero.

b. residuals are normally distributed.

c. variance of the residuals is constant across the range of the data.

**d. All of the above**

3. Consider the following graph of residuals and the regression

line from a time-series regression:

These residuals exhibit the regression problem of:

a. homoskedasticity.

b. multicolinearity.

c. autocorrelation.

**d. heteroskedasticity.**

4. Which of the following is a potential remedy for multicollinearity?

a. Increase the sample size.

b. Take first differences of the dependent variable.

c. Add dummy variables to the regression.

**d. Omit one or more of the collinear variables.**

5. Products that fail a functional test gate get reworked and get sent through this functional test again. Some products go through this cycle multiple times. The manufacturing area is deciding to implement some type of SPC chart to track the number of times each product fails this functional test before being accepted and shipped. Which type of SPC Chart would you suggest to be used?

**a .C-Chart**

b. Individuals and Moving Range Chart

c. P-Chart

d. NP-Chart

6. An MBA class project requires your team to estimate the proportion of people that will vote in the next election. You have no prior knowledge of how many are expected to vote. In order to assure an estimate that falls within five percentage points of error, how many people do you and your team have to survey to achieve this estimate with 95% confidence (assume Normal approximation applies)?

**o 385 people**

o 271 people

o 73 people

o a minimum of 30 people is recommended

7. Product from three production lines is mixed in a final packaging area. Line A is known to be 2% defective, Line B is 4% defective, and Line C is 6% defective. Both Line B and Line C operate at half the manufacturing rate of Line A. What is the expected defect rate of the final shipped material?

**o 3.5% defective **

o 4% defective

o 6% defective

o 12% defective

8. Which of the following are measures of central tendency?

o Mean and Mode

o Mean, Median, Percentile

**o Mean, Median, Mode**

o Mean, Percentile, Mode, Median

9. The statistical technique that allows estimates about population parameters with a known level of certainty is called:

o Control Limits

**o Confidence Intervals **

o Specification Limits

o Action Limits

10. Five samples of a product are tested for power after a reliability testing to assess any degradation. The products measured 10, 10.1, 10.5, 9.8, and 10.7 watts. If the average wattage is greater than or equal to 10 watts at 95% confidence level, we can conclude that the degradation has occurred. Calculate the appropriate statistics and conclude.

**o 1.329, No degradation **

o 2.132, No degradation

o 1.329, Degradation has occurred

o 2. 132, Degradation has occurred