Master of Business Administration in Management
STAT 500 Statistics for Managers
1. Applying Six Sigma total quality management technique learned in the course to your workplace, identify a product or service whose quality needs to be monitored and controlled. (20 %)
a) Set up control chart(s) for the product or service studied.
b) On the basis of your results, indicate whether the process is in control.
c) What is your recommended policy if the process is in control or NOT in control?
2. The PGGW has conducted a statistical analysis of 1,000 long-distance telephone calls made by its customers indicates that the length of these calls is normally distributed with a mean of 240 seconds and standard deviation of 40 seconds. (10 %)
a) What percentage of these calls lasted less than 180 seconds?
b) What is the probability that a particular call lasted between 180 and 300 seconds?
c) What is the probability that a particular call lasted for 30 minutes?
d) What is the length of a particular call if only 1% of the calls are shorter?
3. The Tiger Rock Tunnel management knows that vehicles arrive at the rate of 50 per minute during the 6:00-7:00 P.M. rush hour. If a vehicle has just arrived, (5 %)
a) What is the probability that the next auto arrives within 3 seconds?
b) What is the probability that the next auto arrives within 1 second?
4. The manager of Coca Coca wants to estimate the actual amount of soft drink contained in 1-liter bottles. The company has a specification requirement that the standard deviation of the amount of soft drink is equal to 0.02 liter. A random sample of 50 bottles is selected, and the sample mean amount of soft drink per 1-litre bottle is 0.995 liter. (10 %)
a) Set up a 99% confidence interval, estimate the true population mean amount of soft drink included in a 1-liter bottle.
b) On the basis of your results, do you think the manager has a right to complain to the production manager? Why?
c) Does the population amount of soft drink per bottle have to be normally distributed? Explain.
5) A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 95% confident that the sample mean is correct to within +/- of the true population mean annual family medical expenses. A pilot study indicates that the standard deviation can be estimated as 0. (5 %)
a) How large a sample size is necessary?
b) If management wants to be correct to within +/- , what sample size is necessary?
6) The quality control manager at a lightbulb factory needs to determine whether the mean life of a large shipment of lightbulbs is equal to the specified value of 375 hours. The process standard deviation is known to be 100 hours. A random sample of 64 lightbulbs indicates a sample mean life of 350 hours. (15 %)
a) State the null and alternative hypotheses.
b) At the 0.05 significance level, is there evidence that the mean life is different from 375 hours?
c) Set up a 95% confidence interval, estimate the population mean life of the lightbulbs.
d) What is the relationship between hypothesis testing and confidence interval estimation?
7) A large mail-order house believes that there is an association between the weight of the mail it receives and the number of orders to be filled. It would like to investigate the relationship in order to predict the number of orders based on the weight of the mail. From an operational perspective, knowledge of the number of orders will help in the planning of the order-fulfillment process. A sample of 25 mails shipments is selected within a range of 200 to 700 pounds. The results are as follows: (20 %)
Weight of
Orders
Weight of
Orders
Weight of
Orders
Mail (lbs)
(in 0)
Mail (lbs)
(in 0)
Mail (lbs)
(in 0)
216
6.1
384
10.6
528
16.2
283
9.1
404
12.5
501
15.8
237
7.2
426
12.9
628
19
203
7.5
482
14.5
677
19.4
259
6.9
432
13.6
602
19.1
374
11.5
409
12.8
630
18
342
10.3
553
16.5
652
20.2
301
9.5
572
17.1
365
9.2
506
15
a) Assuming a linear relationship, use the least-squares method to find the regression coefficients, the vertical intercept and the slope.
b) Interpret the meaning of the vertical intercept and the slope.
c) Predict the average number of orders when the weight of the mail is 500 pounds.
d) Is your prediction in ( c ) reliable? Explain
8) Develop a model to predict the assessed value using the size of the houses and the age of the houses from the following table: (15 %)
House
Value
Size (sq ft)
Age
1
844000
2000
3.42
2
774000
1710
11.5
3
757000
1450
8.33
4
859000
1760
0
5
791000
1930
7.42
6
704000
1200
32
7
758000
1550
16
8
859000
1930
2
9
785000
1590
1.75
10
792000
1500
2.75
11
867000
1900
0
12
793000
1390
0
13
745000
1540
12.58
14
838000
1890
2.75
15
768000
1590
7.17
a) State the multiple regression equation.
b) Find the intercept and slopes in this equation.
c) Assess the value of a house that has a size of 1,750 sq ft and is 10 years old.
- End -
Credit:ivythesis.typepad.com
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