الاحصاء الهندسي
SE 325 Engineering Statistics Midterm Exam Sample
- Consider the hypothesis on the mean filling in a filling
operation:
H0:μ = 20 ml
H1:μ ≠ 20 ml
The standard deviation of the filling operation is 2.2 ml. For a sample size equal to 8 and confidence of 0.05, what is the smallest deviation in the mean that this hypothesis can detect with a probability of 0.80? - Nabisco Arabia produces packed biscuits. The quality specifications of the company will qualify a biscuit pack to be acceptable if there are no more than 3 cracked biscuit pieces. Currently, the production runs a manual inspection and they are considering a modern laser measurement inspection machine. From the production line using the manual inspection, a sample of 210 products have been collected and it has been found that 16 of them do not comply with the specifications. From the production line using the laser measurement inspection machine, a sample of 199 products have been collected and it has been found that 6 products do not comply with the specifications.
- Construct an appropriate hypothesis and test whether it is reasonable to assume that the new inspection machine has made any improvement to the production with confidence level equal to 0.05.
- What is the power of the test to detect a difference in the two proportions if the actual proportion of defectives from the manual inspection is 0.07 and it is 0.02 from the laser inspection machine at 0.05 significance level?
- An industrial engineer is interested in whether the run time of
a machine has any effect on the machine’s consumption of electric
power. He observed the machine for random run times and recorded the
electricity consumption in kWh:
Observation Electricity consumption (kWh) Run time (hours) 1 27 6 2 14 2 3 12 1 4 30 7 5 20 3 6 26 4
The industrial engineer assumes that the electricity consumption and run time are linearly related.- Find the regression line by computing the slope and the intercept.
- Calculate the variance of the error.
- Calculate the variance of the slope.
- In the juice production line in Nadec, it has been observed that
production-expiry dates on some juice bottles are printed in unclear
way. The industrial engineer is investigating the effect of the machine
feed rate on the number of misprints. To study and analyze the case, he
observed the machine for different feed rates and counted the number of
misprints, and he come up with the data organized in the following
table:
Observation Number of misprints
(in one thousand)y
Feed rate
(parts per minute)x
1 55 23 2 28 12 3 60 27 4 25 11 5 64 31 He thinks that a linear regression model will be enough to explain the variability in the number of misprints as a function of the feed rate. Compute the necessary parameters and predict the value of the number of misprints for feed rate equal to 10. What is an estimate of the variance of the error? Note: maintain one decimal place.
- Consider the regression model and summations of secret data:
Construct a 95% confidence interval on the intercept. Maintain 2 decimal places.
- In KFUPM Press, a frequent problem occurs when papers come out
of the cutting machine with a deckled edge, as illustrated below:
The Press thinks that the cause of the deckled edge is the humidity level inside the press. They think that installing a dehumidifier will resolve the problem. Before they can decide on purchasing the dehumidifier, they have sought your assistance, as an industrial engineer, to tell them whether the humidity level has any contribution to the number of papers with a deckled edge. They have given you the data from the last 10 days, as shown in the table below:
Number of deckle papers in a day (thousand per one million)
Humidity (%) Day
y
x
1
14
30
2
19
43
3 22
90
4
23
61
5
22
40
6
23
35
7
21
84
8
23
59
9
20
52
10
19
83
How can you assess the Press with this issue? Justify your conclusion. Maintain 2 decimal places.
- The industrial engineer is interested in whether spending more
riyals in the repairs of the production line will reduce the number
of defective parts. To prove any relationship, he monitored the
production line for 15 weeks and recorded how much the production
spent on production line repairs and the number of defective parts
every week. Assuming y for the number of defective parts and x for
the repairs cost, the summery of the data is
n=15; ∑y=14,117; ∑x=7,203; ∑y^2=15,640,721 ∑x^2=4,051,235; ∑xy=5,598,067
Perform the following:
- Test the significance of regression using the analysis of variance at 0.05 confidence level.
- Construct a 95% confidence interval on the expected number of defective parts when the expenditure on repairs is 400 riyals in a month.