This document discusses acceptance sampling plans, which are used to determine if a lot of goods should be accepted or rejected based on inspecting a sample rather than the entire lot. It defines key terms like lot size, sample size, acceptance number, and proportion defective. Acceptance sampling plans aim to balance acceptance probability and producer/consumer risks. The document shows that larger sample sizes result in better representation of the lot and lower risks for both producers and consumers, though returns diminish above a sample size of around 240. It concludes that prevention to improve processes may be better than 100% reliance on acceptance sampling.
Esitmates for year 201620162015Sales (units) increase.docxYASHU40
Esitmates for year 2016
2016
2015
Sales (units) increase
10%
115,000
Sale Price (unit) increase
1%
$5.00
Raw material:
Price
DM - Plasitic (lb.)
$2.90
$3.00
DM - Wheel (wheel)
$0.03
$0.02
Labor cost:
wage rate (airplane)
$0.60
$88,775
total
MOH:
Indirect material (per airplane)
$0.005
Indirect labor (per airplane)
$0.003
utility
$850
factory depreciation
$1,000
$27,000
total
Period cost:
S&A expenses - variable (per airplane)
$0.01
S&A expenses - Fixed
$15,000
$130,000
total
Finished Goods:
beginning (units)
?
desired ending (units)
9%
of yearly sales
15,000
Account receivable
25%
23%
Account payable
25%
23%
Tax rate
30%
30%
Minimun bank account
$50,000
$50,000
What is the break-even in sales units for 2016?
What is the target sale in sales units for 2016 with a target profit of $200,000?
Assuming at the beginning of 2015, the company made the plan same as 2016. Find the quantity factors and price factors for 2015:
Prepare income statement using both variable costing method and absorption costing method for 2016
Prepare a flexible budget for 2016, with decrease 10% sales, same, and increase 10% sales
Prepare a Master Budget for 2016:
Sales budget
Production budget
DM purchases budget
DL cost budget
MOH cost budget
COGS budget
S&A budget
Cash budget
Account receivable
Account payable
Does the factory need to borrow money at the end of 2016?
MS1023 Business Statistics with Computer Applications Homework #4
Maho Sonmez [email protected] 1
MS1023 Business Statistics w/Comp Apps I
Homework #4 – Use Red Par Score Form
Chps. 9 & 10: 50 Questions Only
1. The first step in testing a hypothesis is to
establish a true null hypothesis and a false
alternative hypothesis.
a) True
b) False
2. In testing hypotheses, the researcher
initially assumes that the alternative
hypothesis is true and uses the sample data
to reject it.
a) True
b) False
3. The null and the alternative hypotheses
must be mutually exclusive and collectively
exhaustive.
a) True
b) False
4. Generally speaking, the hypotheses that
business researchers want to prove are stated
in the alternative hypothesis.
a) True
b) False
5. When a true null hypothesis is rejected,
the researcher has made a Type I error.
a) True
b) False
6. When a false null hypothesis is rejected,
the researcher has made a Type II error.
a) True
b) False
7. The rejection region for a hypothesis test
becomes smaller if the level of significance
is changed from 0.01 to 0.05.
a) True
b) False
8. Whenever hypotheses are established
such that the alternative hypothesis is "μ>8",
where μ is the population mean, the
hypothesis test would be a two-tailed test.
a) True
b) False
9. Whene ...
Esitmates for year 201620162015Sales (units) increase.docxYASHU40
Esitmates for year 2016
2016
2015
Sales (units) increase
10%
115,000
Sale Price (unit) increase
1%
$5.00
Raw material:
Price
DM - Plasitic (lb.)
$2.90
$3.00
DM - Wheel (wheel)
$0.03
$0.02
Labor cost:
wage rate (airplane)
$0.60
$88,775
total
MOH:
Indirect material (per airplane)
$0.005
Indirect labor (per airplane)
$0.003
utility
$850
factory depreciation
$1,000
$27,000
total
Period cost:
S&A expenses - variable (per airplane)
$0.01
S&A expenses - Fixed
$15,000
$130,000
total
Finished Goods:
beginning (units)
?
desired ending (units)
9%
of yearly sales
15,000
Account receivable
25%
23%
Account payable
25%
23%
Tax rate
30%
30%
Minimun bank account
$50,000
$50,000
What is the break-even in sales units for 2016?
What is the target sale in sales units for 2016 with a target profit of $200,000?
Assuming at the beginning of 2015, the company made the plan same as 2016. Find the quantity factors and price factors for 2015:
Prepare income statement using both variable costing method and absorption costing method for 2016
Prepare a flexible budget for 2016, with decrease 10% sales, same, and increase 10% sales
Prepare a Master Budget for 2016:
Sales budget
Production budget
DM purchases budget
DL cost budget
MOH cost budget
COGS budget
S&A budget
Cash budget
Account receivable
Account payable
Does the factory need to borrow money at the end of 2016?
MS1023 Business Statistics with Computer Applications Homework #4
Maho Sonmez [email protected] 1
MS1023 Business Statistics w/Comp Apps I
Homework #4 – Use Red Par Score Form
Chps. 9 & 10: 50 Questions Only
1. The first step in testing a hypothesis is to
establish a true null hypothesis and a false
alternative hypothesis.
a) True
b) False
2. In testing hypotheses, the researcher
initially assumes that the alternative
hypothesis is true and uses the sample data
to reject it.
a) True
b) False
3. The null and the alternative hypotheses
must be mutually exclusive and collectively
exhaustive.
a) True
b) False
4. Generally speaking, the hypotheses that
business researchers want to prove are stated
in the alternative hypothesis.
a) True
b) False
5. When a true null hypothesis is rejected,
the researcher has made a Type I error.
a) True
b) False
6. When a false null hypothesis is rejected,
the researcher has made a Type II error.
a) True
b) False
7. The rejection region for a hypothesis test
becomes smaller if the level of significance
is changed from 0.01 to 0.05.
a) True
b) False
8. Whenever hypotheses are established
such that the alternative hypothesis is "μ>8",
where μ is the population mean, the
hypothesis test would be a two-tailed test.
a) True
b) False
9. Whene ...
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Empowering the Data Analytics Ecosystem: A Laser Focus on Value
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2. Rationale: (I don’t buy the argument,
but…….)
In situations where Producers and Consumers
are willing to put up with shipments of goods
which contain defects, the issue then becomes
how to keep Lots (shipments) with an
“excessive” number of defects from being
accepted. In order to keep Appraisal costs
down, sampling schemes are devised to
sample items from the Lot and then to accept
or reject the Lot based upon the number of
defective items found in the sample.
2
3. Notation
• N= number of items in the Lot.
• n= number of items in the random sample of
items taken from the Lot.
• D= number (unknown) of items in the Lot which
are defective.
• r= number of defective items in the random
sample of size n.
• c= acceptance number; if r is less than or equal to
c then the Lot is deemed to be of Acceptable
Quality, otherwise the Lot is rejected.
3
4. Acceptance Sampling Plan
An Acceptance Sampling Plan is defined by:
• N= Lot size
• n=sample size
• c=acceptance number
4
5. Acceptance Probability and Risks
Assuming:
We can evaluate a sampling plan with its
corresponding Operating Characteristic Curve, a.k.a.
OC curve.
( ) P( _ _ _ _ )
a
P p accept lot with p proportion defective
p D N
5
6. Calculating probabilities for the
OC curve
The probabilities used in calculating values for the
OC curve are calculated using the Hypergeometric
Distribution. Given that
then the probability that the number of defectives in
the sample of size n is equal to r is given by
p D N
N D D
n r r
N
n
6
7. Acceptable Quality Level-AQL
If the Lot has a proportion of defectives lower
than the AQL, i.e.
then the Lot is deemed to be of Acceptable
Quality Level by Producer and Consumer.
p AQL
7
8. OC curve and Producer and Consumer Risk
The Probability that we accept a Lot is
for a given proportion of defectives
which is calculated using the Hypergeometric
Distribution as given.
a
P p P r c
p D N
8
9. Risks and the AQL
• If the proportion defective is less than or
equal to the AQL, then the Producer runs the
risk of having the Lot rejected which is:
• If the proportion of defectives is greater than
the AQL, then the Consumer runs the risk of
accepting a Lot of unacceptable quality which
is:
1 ,
a
P p p AQL
,
a
P p p AQL
9
10. Suppose AQL=5%
If the AQL=5%, we might think that the
sample proportion which does not exceed 5%
would indicate that the Lot is acceptable. Let
us suppose our Lot size=1,000. If we plot
we can see how well various plans work.
( _ ) . _
a
P P Accept Lot vs p proportion defective
10
12. They can work if………
• If the Lots are either really good (very few
defects), or really bad (many defectives).
• The samples are “representative”, i.e. close to
the true proportion of defectives.
“Representative” is not the same as “random”.
• Random samples are chosen in such a way
that every possible subset is equally likely.
• Only large samples are likely to be
representative.
12
13. Producer and Consumer Risks
• If n=20, the producer’s risk at the AQL is
around 30%, i.e. a Lot of acceptable quality
may be rejected.
• At just over 5% defective, the Consumer’s risk
is about 70%.
• The plans work better as n increases.
13
14. When does random sampling start to
work well?
• As n increases, we would expect the
Producer’s and Consumer’s risk to both
decrease.
• How much do we have to sample to reach an
“acceptable level” of risk for both of them.
14
16. More sampling clearly does work
• If we compare n=20 to n=100, there is a
substantial improvement.
• If we compare n=100 to n=240, there is still
an improvement, but the amount of
improvement is not as great, i.e. there is a
diminishing return.
16
18. Largest sampling plans comparison
• The largest sampling plan, n=500 has the best
performance in terms of risk, but it is not
much better than n=100 or n=240.
• The only way to get no risk is to sample
everything, or…..
• Invest in Prevention, then only use sampling
to monitor the improved processes.
18