Forecast uncertain demand products
Choose the suitable place for production
Better forecast
Use both quantitative + qualitative method
Analyze historical data => forecast future trend
Use weighted factors (weighted average independent forecasts)
Shorten forecasting duration
Forecast uncertain demand products
Choose the suitable place for production
Better forecast
Use both quantitative + qualitative method
Analyze historical data => forecast future trend
Use weighted factors (weighted average independent forecasts)
Shorten forecasting duration
This presentation describes the journey of Louis Vuitton in Japan. It highlights the strategies adopted by Louis Vuitton to beat the competition in the fiercely competitive luxury market of Japan
This presentation describes the journey of Louis Vuitton in Japan. It highlights the strategies adopted by Louis Vuitton to beat the competition in the fiercely competitive luxury market of Japan
Statistics practice for finalBe sure to review the following.docxdessiechisomjj4
Statistics practice for final
Be sure to review the following and have this information handy when taking Final GHA:
· Calculating z alpha/2 and t alpha/2 on Tables II and IV
· Find sample size for estimating population mean. Formula 8.3 p. 321 OCR.
· Stating H0 and H1 claims about variation and about the mean. Chapter 9 OCR.
· Type I and Type II errors p. 345 OCR.
· Confidence Interval for difference between two population means. Chapter 10 OCR p. 428
· Pooled sample standard deviation. Chapter 10 OCR p. 397
· What do Chi-Square tests measure? How are their degrees of freedom calculated? Chapter 12 OCR
· Find F test statistic using One-Way ANOVA.xls Be sure to enable editing and change values to match your problem. One-Way ANOVA.xls
· Find equation of regression line used to predict. To do on Excel, go to a blank worksheet, enter x values in one column and their matching y values in another column. Click Insert – Select Scatterplot. Right click any one of the points (diamonds) on the graph. Left click “Add a Trendline.” Check “Display Equation on Chart” box. Regression equation will appear on chart. Try it here with No. 20 below.
Practice Problems
Chapter 8 Final Review
1) In which of the following situations is it reasonable to use the z-interval
procedure to obtain a confidence interval for the population mean?
Assume that the population standard deviation is known.
A. n = 10, the data contain no outliers, the variable under consideration is
not normally distributed.
B. n = 10, the variable under consideration is normally distributed.
C. n = 18, the data contain no outliers, the variable under consideration is
far from being normally distributed.
D. n = 18, the data contain outliers, the variable under consideration is
normally distributed.
Find the necessary sample size.
2) The weekly earnings of students in one age group are normally
distributed with a standard deviation of 10 dollars. A researcher wishes to
estimate the mean weekly earnings of students in this age group. Find the
sample size needed to assure with 95 percent confidence that the sample
mean will not differ from the population mean by more than 2 dollars.
Find the specified t-value.
3) For a t-curve with df = 6, find the two t-values that divide the area under
the curve into a middle 0.99 area and two outside areas of 0.005.
Provide an appropriate response.
4) Under what conditions would you choose to use the t-interval procedure
instead of the z-interval procedure in order to obtain a confidence
interval for a population mean? What conditions must be satisfied in
order to use the t-interval procedure?
CHAPTER 8 Answers
1) B
2) 97
3) -3.707, 3.707
4) When the population standard deviation is unknown, the t-interval procedure is used instead of the
z-interval procedure. The t-interval procedure works provided that the population is normally
distributed or the.
FOR MORE CLASSES VISIT
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1. The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.2 miles per gallon.
Part 1 of 16 -Question 1 of 231.0 PointsThe data presented i.docxodiliagilby
Part 1 of 16 -
Question 1 of 23
1.0 Points
The data presented in the table below resulted from an experiment in which seeds of 5 different types were planted and the number of seeds that germinated within 5 weeks after planting was recorded for each seed type. At the .01 level of significance, is the proportion of seeds that germinate dependent on the seed type?
Seed Type
Observed Frequencies
Germinated
Failed to Germinate
1
31
7
2
57
33
3
87
60
4
52
44
5
10
19
Reset Selection
Question 2 of 23
1.0 Points
A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.
Machine
Shift
A
B
C
D
1
41
20
12
16
2
31
11
9
14
3
15
17
16
10
Reset Selection
Part 2 of 16 -
Question 3 of 23
1.0 Points
In choosing the “best-fitting” line through a set of points in linear regression, we choose the one with the:
Reset Selection
Question 4 of 23
1.0 Points
A single variable X can explain a large percentage of the variation in some other variable Y when the two variables are:
Reset Selection
Question 5 of 23
1.0 Points
A correlation value of zero indicates.
Reset Selection
Part 3 of 16 -
Question 6 of 23
1.0 Points
An investor wants to compare the risks associated with two different stocks. One way to measure the risk of a given stock is to measure the variation in the stock’s daily price changes.
In an effort to test the claim that the variance in the daily stock price changes for stock 1 is different from the variance in the daily stock price changes for stock 2, the investor obtains a random sample of 21 daily price changes for stock 1 and 21 daily price changes for stock 2.
The summary statistics associated with these samples are: n
1
= 21, s
1
= .725, n
2
= 21, s
2
= .529.
If you compute the test value by placing the larger variance in the numerator, at the .05 level of significance, would you conclude that the risks associated with these two stocks are different?
Reset Selection
Question 7 of 23
1.0 Points
Two independent samples of sizes n
1
= 50 and n
2
= 50 are randomly selected from two populations to test the difference between the population means,
. The sampling distribution of the sample mean difference,
is:
Reset Selection
Part 4 of 16 -
Question 8 of 23
1.0 Points
Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 7.7 seconds. What would you use for the alternative hypothesis?
Reset Selection
Question 9 of 23
1.0 Points
A two-tailed test is one where:
Reset Selection
Question 10 of 23
1.0 Points
Which of the following values is not typically used for
?
Reset Selection
Part 5 of 16 -
Question 11 of 23
1.0 Points
From a sample of 500 items, 30 wer.
FOR MORE CLASSES VISIT
www.qnt561genius.com
1. The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.2 miles per gallon.
FOR MORE CLASSES VISIT
www.qnt561genius.com
1. The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.2 miles per gallon.
Cracking the Workplace Discipline Code Main.pptxWorkforce Group
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• Four (4) workplace discipline methods you should consider
• The best and most practical approach to implementing workplace discipline.
• Three (3) key tips to maintain a disciplined workplace.
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In this comprehensive presentation, we will explore strategies and practical tips for enhancing profitability in small businesses. Tailored to meet the unique challenges faced by small enterprises, this session covers various aspects that directly impact the bottom line. Attendees will learn how to optimize operational efficiency, manage expenses, and increase revenue through innovative marketing and customer engagement techniques.
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It is a sample of an interview for a business english class for pre-intermediate and intermediate english students with emphasis on the speking ability.
2. Session objective
Case 1 : Inferences about a single population variance
Case 2 : Inference about two population variance
Case 3 : Testing equality of three or more proportions
Case 4: Test of independence for three or more
population
3. Case 1 : Inferences about a
single population variance
4. Case 1 : Inferences about a population variance
Where 𝑠2𝑖𝑠 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
n= no: of samples
𝜎0
2
= 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒
5.
6. The st. louis Metro bus company wants to promote an image of reliability by
encouraging its drivers to maintain consistent schedules. as a standard policy the
company would like arrival times at bus stops to have low variability. in terms of the
variance of arrival times, the company standard specifies an arrival time variance of
4 or less when arrival times are measured in minutes. the following hypothesis test is
formulated to help the company determine whether the arrival time population
variance is excessive. test using a level of significance of a = .05.
Suppose that a random sample of 24 bus arrivals taken at a downtown
intersection provides a sample variance of 𝜎2 = 4.9. Assuming that the
population distribution of arrival times is approximately normal, the
value of the test statistic is as follows.
7. • Because this is an upper tail test, the area under the curve to the right of
the test statistic x2 = 28.18
• The critical value of Chi for 𝛼 =
0.05 𝑎𝑛𝑑 23 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑓𝑟𝑒𝑒𝑑𝑜𝑚 = 35.172
• Reject 𝐻0 𝑖𝑓 𝑋2
≥35.172 because the value of the test
statistic is 𝑋2 = 28.18, we cannot reject the null hypothesis.
The sample does not support the conclusion that the
population variance of the arrival times is excessive.
8. Pg 657 Q 12
A Fortune study found that the variance in the number of vehicles owned or
leased by subscribers to Fortune magazine is .94. assume a sample of 12
subscribers to another magazine provided the following data on the number
of vehicles owned or leased: 2, 1, 2, 0, 3, 2, 2, 1, 2, 1, 0, and 1
a) Compute the sample variance in the number of vehicles owned or leased by
the 12 subscribers.
b)Test the hypothesis 𝐻0: 𝜎2 = .94 to determine whether the variance in the
number of vehicles owned or leased by subscribers of the other magazine
differs from 𝜎2 = .94 for Fortune. at a .05 level of significance, what is your
conclusion?
9. 𝛼 = .05 , two tail , df = 11 Chi square table value =21.92 ; ,
cannot reject H0.
The variance in the number of vehicles owned or leased by
subscribers of the other magazine does not differ from 𝜎2
=
.94
10. Case 2 : Inference about
two population variance
11. F distribution - test statistic for hypothesis
tests about Population Variances
the F distribution is based on sampling from two normal populations.
whenever independent simple random samples of sizes 𝑛1and 𝑛2 are selected from two
normal populations with equal variances, the sampling distribution of
F=
𝑆1
2
𝑆2
2
is an F distribution with
𝑛1 − 1 degrees of freedom for the numerator
𝑛2 − 1 degrees of freedom for the denominator
𝑆1
2
is the sample variance for the random sample of n1 items from population 1
𝑆2
2
is the sample variance for the random sample of n2 items from population 2
12. Note : a one-tailed hypothesis test about two population variances will always be formulated as an upper tail test
To read Fcrit use page 8 from
table
13. Pg 663 Q 16
Investors commonly use the standard deviation of the monthly percentage
return for a mutual fund as a measure of the risk for the fund; in such cases,
a fund that has a larger standard deviation is considered more risky than a
fund with a lower standard deviation. the standard deviation for the
American century equity growth fund and the standard deviation for the
fidelity growth Discovery fund were recently reported to be 15.0% and
18.9%, respectively. assume that each of these standard deviations is based on
a sample of 60 months of returns. Do the sample results support the
conclusion that the fidelity fund has a larger population variance than the
American century fund? which fund is more risky?
14. F crit for df =59 for 𝑛1 and 𝑛2 and 𝛼 = .05 𝑖𝑠 1.40 or 1.39
reject H0. We conclude that the Fidelity fund has a greater variance than the American Century
fund.
15. Q 17 Pg 663
Most individuals are aware of the fact that the average annual repair cost for an
automobile depends on the age of the automobile. a researcher is interested in
finding out whether the variance of the annual repair costs also increases with the
age of the automobile. a sample of 26 automobiles 4 years old showed a sample
standard deviation for annual repair costs of $170 and a sample of 25 automobiles
2 years old showed a sample standard deviation for annual repair costs of $100.
a. State the null and alternative versions of the research hypothesis that the
variance in annual repair costs is larger for the older automobiles
b. At 𝛼= .01 level of significance, what is your conclusion? what is the p-value?
Discuss the reasonableness of your findings
16. F crit for df pf 25 and 24 and 𝛼 = .01 is 2.58
reject H0. Conclude that 4 year old automobiles have a larger variance in
annual repair costs compared to 2 year old automobiles. This is
expected due to the fact that older automobiles are more likely to have
some more expensive repairs which lead to greater variance in the
annual repair costs.
17. Case 4: Test of
independence
for three or more population
18. Chi – square – Test of
independence
One sample from a population and record the observations for two or more
categorical variables.
Summarize the data by counting the number of responses for each combination
of a category for variable 1 and a category for variable 2.
The null hypothesis for this test is that the two categorical variables are
independent.
Example
H0: Variable represented in row is independent of variable represented in
column
H1: Variable represented in row is dependent on variable represented in column
20. Example chi square data and
hypothesis
𝑆𝑡𝑒𝑝 1 ∶ 𝐻0: 𝐵𝑒𝑒𝑟 𝑝𝑟𝑒𝑓𝑒𝑟𝑛𝑐𝑒 𝑖𝑠 𝑖𝑛𝑑𝑒𝑝𝑛𝑑𝑒𝑛𝑡 𝑜𝑓 𝑔𝑒𝑛𝑑𝑒𝑟
𝐻𝑎: 𝐵𝑒𝑒𝑟 𝑝𝑟𝑒𝑓𝑒𝑟𝑛𝑐𝑒 𝑖𝑠 𝑑𝑒𝑝𝑛𝑑𝑒𝑛𝑡 𝑜𝑓 𝑔𝑒𝑛𝑑𝑒𝑟
Note : Ho is Mean of male preference = mean of female preference hence independent of any other factors
Step 2
21. Step 3 : The expected frequency for row i and column j is given by
Male Female
Light
90∗132
200
=59.4
90∗68
200
=30.6 90
Regular
77∗132
200
=50.82
77∗68
200
=26.18 77
Dark
167∗132
200
=110.2
2
167∗68
200
=56.78 167
132 68 200
22. Step 4
Step 5
Df = (r – 1)(c – 1) = (3-1)(2-1) =2 With a = .05 and 2 degrees of freedom,𝑋2 = 5.991, reject H0 if ≥ 5.991 With 6.45 ≥
5.991, we reject H0.
23. Example – Chi square as test of
independence
A research worker conducted survey in two areas and classified some people in income groups on the basis of
sampling studies. Their results are as follows
Test if the areas and income level have association
Solution
H0: The areas and income level are independent or no association
Investigators Poor income Middle
income
High income Total
Area 1 160 30 10 200
Area 2 140 120 40 300
Total 300 150 50 500
X2 = 55.54 , df =2, 5% , crtical = 5.991
CV > TV reject Ho : the areas and income as depe
Kothari Pg 242
24. Example 2
A brand manager is concerned that her brands share may be unevenly distributed throughout the country. In a
survey in which the country was divided into four geographic regions, a random sampling of 100 customers
was conducted with following results. Test at 5% whether the brand share is the same across all regions
X 2 =5.012 , df = 3 , 5% tv = 7.815
cv< tv accept H0
Levin pg 534
North east North west South east South west Total
Purchase the
brand
40 55 45 50 190
Do not purchase
the brand
60 45 55 50 210
Total 100 100 100 100 400
H0: Region is independent of
purchasing or no association
H1: region is dependent of
purchasing
25. Case 3 : Testing equality
of three or more
proportions
27. Q24 Pg 674
The sample data below represent the number of late and on time
flights for Delta, united, and U S airways (Bureau of transportation
statistics, March 2012)
a. Formulate the hypotheses for a test that will determine if the
population proportion of late flights is the same for all three
airlines.
b. Conduct the hypothesis test with a .05 level of significance. what
is your conclusion?
c. Compute the sample proportion of late flights for each airline.
What is the overall proportion of late flights for the three airlines?
28.
29. df =2 Alpha = .05 Critical value of chi square =
5.991
do not reject H0. We are unable to reject the null
hypothesis that the population proportions are the
same.