is this possible

QUESTION ONE

(a)The actual demand of a product for six months is summarized in the table below:

Month (t)Demand D_t

180

290

370

4100

570

690

i. Find three months weighted moving averages by assuming the weights, W₁=0.1, W₂= 0.4 and W₃= 0.5

ii. Compute the mean forecast error

iii. Compute the mean square error (MSE)

iv. Compute the mean absolute deviation (MAD)

v. Mean absolute percent error (MAPE)

(b)The forecast of a product for the first week of January was 200 units, whereas the actual demand turned out to be 220 units.

i. Find the forecast for the week of January assuming the smoothing constant = 0.2

ii. Find the forecast for the third week of third week of January if the actual demand of the second week is 210 units

(c)A supermarket chain purchases large quantities of white bread for sale during a week. The stores purchase the bread for K9.75 per loaf and sell it for K13.10 per loaf. Any loaves not sold by the end of the week can be sold to a local thrift shop for K5.40. Based on past demand, the probability of various levels of demand is as follows:

Demand(loaves)Probability

6,0000.10

8,0000.50

10,0000.30

12,0000.10

(i) Construct a payoff table, indicating the events and alternative courses of action.

(ii) Construct a decision tree.

(iii). Compute the expected monetary value (EMV) for purchasing 6,000, 8,000, 10,000 and 12,000 loaves.

(iv). Compute the expected opportunity loss (EOL) for purchasing 6,000, 8,000, 10,000, and 12,000 loaves.

(v) Based on the results of (iii) or (iv), how many loaves would you purchase? Why?

(vi). Compute the coefficient of variation for each purchase level.

(vii) Compute the return-to-risk ratio (RTRR) for each purchase level.

(viii) Based on (vi) and (vii), what action would you choose? Why?

QUESTION TWO

(a) A large steel manufacturing company has three options with regard to production:

(1) Produce commercially

(2) Build pilot plant

(3) Stop producing steel

The management has estimated that their pilot plant, if built has 0.8 chance of high yield

and 0.2 chance of low yield. If the pilot plant does show a high yield, management assigns a probability of 0.75 that the commercial plant will also have a high yield. If the pilot plant shows a low yield, there is only a 0.1 chance that the commercial plant will show a high yield. Finally, management's best assessment of the yield on a commercial size plant without building a pilot plant first has 0.6 chance of high yield. A pilot plant will cost K300,000. The profits earned under high and low yield conditions are K12,000,000 and K1,200,000 respectively.

i. Draw up an appropriate decision tree for the steel manufacturing company

ii. What is the company's best strategy under EMV approach?

(b)A tea company appoints four salesmen A, B, C and D and observes their sales in three months, April, May and June:

MONTHSSALESMEN

ABCD

April36362135

May28293132

June26282929

I. two - way analysis of variance table

ii. Name the blocking variable and the treatment in this experiment.

iii. Test at the 5% level of significance the null hypothesis that there is significant

difference in sales made by the four salesmen.

iv. Test at the 5% level of significance the null hypothesis that there is significant

difference in the sales made during different months.

QUESTION THREE

Energy consumption is claimed to be a good predictor of Gross National Product. An economist recorded the energy consumption (x) and the Gross National Product (y) for eight countries. The data are shown in the table below:

Energy Consumption (x)3.47.712.0755867113131

Gross National Product (y)5524039011001390133014001900

i. Find the least squares equation for the data.

ii. Estimate the Gross National Product,y, of a country that has an energy consumption of 100.

iii. Estimate the energy consumption of a country that has a Gross National Product of 3500.

iv. Determine at the 5% level of significance whether there is evidence to indicate a linear relationship between energy consumption,x, and Gross National Product,y.

v. Find a 95% confidence interval for _1.

vi. Find the correlation coefficient,r.

vii. Find the coefficient of determination and interpret its value.

viii. Give the ANOVA table for this problem.

QUESTION FOUR

(a) Three suppliers provide the following data on defective spare parts.

SUPPLIERPART QUALITY

GoodMinor DefectMajor Defect

A9037

B170187

C13569

(i) use =0.05 and test for independence between supplier and spare part quality.

(ii) What does the result of your analysis tell the purchasing department?

(b)A new fly spray is applied to 50 samples each of 5 flies and the number of living flies

counted after an hour. The results were as follows:

Number Living012345

Frequency72012911

i. Calculate the mean number of living flies per sample and hence an estimate forp, the probability of a fly surviving the spray

ii. Using your estimate calculate the expected frequencies (each correct to one decimal

place) corresponding to a binomial distribution

iii. Perform a chi - square goodness - of - fit test using a 5% significance level.

(c)A worker earned K11, 800 per month in 2016. The cost of living index increased by 63.8% between 2016 and 2019. How much extra income should the worker have earned in 2019 so that he could buy the same quantities as in 2016?

QUESTION FIVE

(a) Define the following terms:

i. Index number

ii. Time series

(b)The following data relate to the price of rice per kg.in different years.

Year19981999200020012002200320042005

Price in K677810141213

Find out price relative

i. Taking 1998 as base

ii. Taking 2002 as base

iii. Taking average of 1998, 1999 and 2000 as the base

(c)The following table gives the prices of some food items in the base year and current year and the quantities sold in the base year and current year.

Commodity20002005

Price(K)quantityPrice(K)quantity

A15152212

B205274

C41075

Compute the following price index numbers for 2005 from the above table:

i. Laspeyre's price index number

ii. Paasche's price index number

(d)Calculate five -yearly moving averages of the number of students studying in a university and short -term fluctuations from the following figures.

Year19711972 1973197419751976 1977197819791980198119821983

Production.(tonnes)105107109112114116118121123124125127129

1. Devise a null and alternative hypothesis, then perform a t-test using alpha=0.05 if our class is taller or shorter than the average human in the United States. Graphically display your answer and statistically write up results. In addition, determine the effect size of this relationship and interpret.
3. Notes:
4. The average height of adults in the United States is 67.03.8 inches. (Note: this is a population SD)
5. Calculate and interpret the effect size (use Cohen's d):
6. Cohen's d = (Msample- population) )
7. Devise a null and alternative hypothesis, then perform a t-test using alpha =0.05 if the students in our class that are born in warm weather months are taller or shorter than those born in cold weather months. Graphically display your answer and statistically write up results. In addition, determine the effect size of this relationship and interpret.
9. Notes:
10. Population SDs are unknown.
12. Assume the northern hemisphere:
13. Warm months = April, May, June, July, August, September
14. Cold months = October, November, December, January, February, March
16. Use Cohen's d effect size:
17. Cohen's d = (M2- M1) SDpooled) where SDpooled= ((SD12+ SD22) 2)

You will need the data le "sales" for completing this exercise. The le has the

following columns that are relevant to this exercise:

SalesPerSF: Sales per square foot of stores operated by a retail chain,

Income: the median household income in the surrounding community (dollars),

Population000: and the size of the community (in thousands).

Market: This is a qualitative variable. There are 3 types of geographic locations:

urban, suburban, and rural. Two dummy variables have been set up, UrbanDummy

and SuburbanDummy. Rural is selected as the base level.

Disregard the other columns in the le.

(a) Run a regression using SalesPerSF as the dependent variable, and Income, Population000,

and the two dummy variables as predictors. Which of the coecients are

signicantly dierent from zero?

(b) Predict the sales per square foot for a store located in a suburban community

with median household income $71,000, and population size equal to 500,000 people.

what is the95% prediction interval and a 95% condence interval. Explain the dierence

between the two intervals.

(c) Interpret all four coecients in the estimated regression equation.

SalesPerSF544.3 481.2 527.5 550.5 561.1 491.1 691.7 483.5 572.6 582 403.3 612.8 489.1 481 441.5 573.8 467.9 607.6 508.9 587.4 393.4 564.2 588.3 569.4 641.9 646.4 490.1 616.5 467.1 630.2 532.9 353.2 580.2 379.3 495.8 468.4 362.9 355.8 455.9 382 476.2 376.8 341.4 428 465.5 475.7 442 469.3 555.2 401.7 488.8 512 437.9 417.5 352.7 416.7 283.5 454 466.6 461.1 376 162.8 458.3 325.7 313.1 305.1 276.6 310.5 272.7 425.6 468.4 209.4 126.9 325.9 442.9 458.2 409.9 349.2 471.4 476.4 407.5 375.1 319.8 287.2 518.1 213.8 290.9

Income89000 78000 71000 64000 69000 59000 76000 59000 64000 76000 61000 73000 68000 84000 78000 76000 78000 72000 67000 71000 65000 52000 72000 73000 88000 78000 67000 69000 61000 79000 75000 52000 71000 86000 84000 86000 80000 73000 74000 84000 87000 85000 77000 70000 90000 80000 74000 86000 73000 71000 93000 71000 95000 76000 75000 73000 64000 92000 78000 79000 63000 50000 64000 58000 62000 54000 65000 65000 59000 70000 72000 62000 55000 74000 66000 69000 60000 56000 67000 56000 63000 66000 66000 56000 63000 63000 65000

Population(000)503 463 597 452 684 610 699 663 760 569 685 872 712 514 326 769 421 499 672 1077 710 592 829 650 755 531 559 726 581 531 470 551 482 849 796 713 578 798 786 740 850 828 729 926 641 953 862 1224 992 626 947 1075 884 1034 827 985 635 424 923 793 612 560 452 611 433 705 658 438 434 552 656 410 321 270 738 548 774 646 831 947 945 323 260 401 628 222 395

MarketUrban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Suburban Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural

BONUS QUESTION

Question:

QUESTION 1

State the null hypothesis and alternate hypothesis for the following:

The publisher ofCelebrity Livingclaims that the mean sales of personality magazines featuring celebrities such as Angelina Jolie or Kim Kardashian is greater than 1.5 million per week. A sample of 10 comparable titles shows that the mean weekly sales last week was 1.3 million. The publisher's claim of 1.5 million per week is to be verified.

In the first blank, state the sign, and in the second blank, state the number.

Use the following to enter your sign:

= for equals/= for does not equal to

>for greater than>= for greater than or equal to

SignNumber

H₀: ___________________million

H₁: ___________________million

QUESTION 2

State the null hypothesis and alternate hypothesis for the following:

An online retailer ships product from overseas with an advertised delivery date stating less than 10 days. To test whether or not deliveries are made within the advertised time, a random sample of 36 orders is selected from a normal population. The sample mean delivery time is 12 days and the known population standard deviation is 3 days.

In the first blank, state the sign, and in the second blank, state the number.

Use the following to enter your sign:

=equals/=does not equal to

>greater than>=greater than or equal to

SignNumber

H₀: ___________________days

H₁: ___________________days

QUESTION 3

State the null hypothesis and alternate hypothesis for the following:

A machine on a production line is set to automatically fill each bottle with 500 mLof water. The quality control manager regularly takes random samples of the bottles from the production line to ensure that the machine is filling the bottles correctly. If not, the machine will need adjusting.

In the first blank, state the sign, and in the second blank, state the number.

Use the following to enter your sign:

=equals/=does not equal to

>greater than>=greater than or equal to

SignNumber

H₀: ___________________mL

H₁: ___________________ mL

QUESTION 4

Use the following for thenext4questions:

A recent national survey found that high school students watched an average of 6.8DVDsper month with a population standard deviation of 0.5 hours. The distribution of times follows the normal distribution. A random sample of 36 college students revealed that the mean number ofDVDswatched last month was 6.2. At the 0.05 significance level, can we conclude that college students watch fewerDVD'sa month than high school students (average of 6.8 DVDsper month)?

H₀: 6.8

H₁: < 6.8

1)What kind of test is this?