Home Work Assignment 6

for MSIS 385 section 01

Last modified on 12/14/99

Due December 19 1999

Note:

This assignment is optional. It is worth only 50 points. If you choose to hand it in it will be averaged with the rest of your assignments. If you don't your five assignments will be averaged.

If you choose to hand in this assignment I prefer to get it by e-mail to alizadeh@andromeda.rutgers.edu. Otherwise you may put the files in a diskette and leave it in my mailbox on the second floor of Janice Levin building.

Create an excel file and put the answer to each question in a separate worksheet. attach the excel file to your e-mail or put it on your floppy disk.

Reading material for ANOVA topic: 14.1-14.4.6.



Question 1

In computers programs that generate random numbers are generated according to some rule, which generates numbers that look random. Thus it is necessary to examine number generated by computers. A computer program is supposed to generate numbers {1,3,5,7,9,11} randomly according to the distribution given below. Each time you run this program one of the numbers 1,3,5,7,9, or 11 is returned, supposedly randomly with probabilities defined:





number

1

3

5

7

9

11

probability

1/10

1/5

3/10

1/10

1/5

1/10




To test the quality of this program you run it 1000 times and tabulate the number of times each number is generated as follows:



number

1

3

5

7

9

11

frequency

98

207

296

102

203

94




Based on these observations determine if this data is too good to be considered truly random. Use P-value method and confidence level of 95%.









Question 2

A home gardener wants to determine the effect of different fertilizers on the average number of tomatoes produced by her plants. She grows five tomato plants on each of four separate plots and uses different fertilizer treatment on each plot. The number of tomatoes per plant are indicated in the table below:



plot 1

14

10

12

16

17

plot 2

9

11

12

8

10

plot 3

16

15

14

10

18

plot 4

10

11

11

13

8



3a

Using Excel's one-way ANOVA tool determine at 5% significance level if there is difference among various plots. Assume number of tomatoes per plant is approximately normal and variance among plots are approximately equal.

3b

If answer to part a is rejection of the null hypothesis, use Tuckey's method to determine which pairs produce significantly different means at 5% level.



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