# FIT a straight line trend by the method of least squares to the following data. Assuming that the same rate of change continues, what would be the predicted earnings for the year 2008

Quantitative Techniques Assignment

1. FIT a straight line trend by the method of least squares to the following data. Assuming that the same rate of change continues, what would be the predicted earnings for the year 2008?
 Year 1999 2000 2001 2002 2003 2004 2005 2006 Earning  in thousand shillings 28 30 55 62 59 50 77 85

1. 12 students were given intensive coaching and 5 tests were conducted in a month. The scores of tests 1 and 5 are given below. Do the scores from the tests show an improvement?
 No. of students 1 2 3 4 5 6 7 8 9 10 11 Marks in 1st test 50 42 51 26 35 42 60 41 70 55 62 Marks in 5th test 62 40 61 35 30 52 68 51 84 63 72

1. The number of defects per unit in a sample of 330 units of a manufactured product was found as follows:
 Number of defects 0 1 2 3 4 Number of units 214 92 20 3 1

Fit a poissson distribution to the data and test for goodness of fit.

1. In the accounting department of a bank 100 accounts are selected at random and examined for errors. Suppose the following results have been obtained.
 No of error 0 1 2 3 4 5 6 7 No of accounts 35 40 19 32 0 23 2 2

On the basis of this information can it be concluded that the errors are distributed according to the Poisson probability law?                                                                                                                              (7 Marks)

1. A multiple-choice test consists of 8 questions with 3 answers to each question (of which one is correct). A student answers each question by rolling a balanced dice and checking the first answer if he gets 1 or 2, the second answer if he gets 3 or 4 and the third answer if he gets 5 or 6. To get a distinction, the student, the student must secure at least 75% correct answers. If there is no negative marking, what is the probability that the student secures distinction?                                                   (7 Marks)
2. A trader alleges that the items he sales weigh 20.5 kgs. To confirm it, a sample of size 7 of items was taken and weight and found to weigh 15,17,19,18,21,16,18. Test the trader assertion at 5% significance level. The relevant extract of t value is given below.
 T one tail 0.01 0.05 0.025 Two tail 0.02 0.1 0.05 Df    6 3.143 1.943 2.447 Df    7 2.998 1.895 2.365

(7 Marks)

1. There are 800 in Nairobi campus of Moi University and the probability for any student to need a copy of a particular textbook from the library on any day is 0.05. How many copies of the book should be kept in the university library so that the probability may be greater than 0.9 that none of the students needing a copy from the library has to come back disappointed. (use normal approximation to the binomial probability law) (4 marks)
2. A manufacturer who produces fresh juice bottles, find that 0.21% of the bottles are defective. The bottles are packed in boxes containing 500 bottles. A soft drink manufacturer buys 200 boxes from the producer of bottles. Using poisson distribution, find how many boxes will contain;
3. No defective
4. At least three defective (given e-0.5=0.6065) (4 marks)

1. Fit a straight line trend by the method of least squares to the following data. Assuming that the same rate of change continues, what would be the predicted earnings for the year 2008?
 Year 1999 2000 2001 2002 2003 2004 2005 2006 Earning  in thousand shillings 28 30 55 62 59 50 77 85

(10 marks)

1. A trader alleges that the items he sales weigh 20.5 kgs. To confirm it, a sample of size 7 of items was taken and weight and found to weigh 15,17,19,18,21,16,18. Test the trader assertion at 5% significance level. The relevant extract of t value is given below.
 T one tail 0.01 0.05 0.025 Two tail 0.02 0.1 0.05 Df    6 3.143 1.943 2.447 Df    7 2.998 1.895 2.365

[10 marks]

1. The average monthly sales of 5000 firms are normally distributed. Its mean and standard deviation are kshs. 72000 and kshs. 20000 rspectively. Find
2. The number of firms the sales of which are over 50000
3. The percentage of firms the sales of which will be between kshs. 73000 and kshs. 85000
• The number of the firms the sales of which will be between kshs. 60000 and Kshs. 75000. The relevant extract at the area table (under normal curve) is given below
 Z 0.05 0.15 0.6 0.65 1.1 Area 0.0199 0.0596 0.2257 0.2422 0.3643

(11 marks)

1. A manufacturer of a certain electronic tube claims that the average life span of tubes will exceed 1000 hrs. From past experience the standard deviation is known to be 120 hrs. A retailer is willing to order for a large consignment if the manufacturer’s claim is true. The retailer gets a sample of 36 tubes tested and finds that the sample mean life span is 1040 hrs. (a) should the retailer order for the consignment at α =0.05 level of significance (b) at α = 0.01 level of significance?

1. The data about the number of units of production per day turned out by 4 different workers using 5 different types of machines are:
 WORKERS MACHINE TYPE A B C D 1 88 76 94 72 2 92 80 104 86 3 68 72 88 64 4 86 76 92 66 5 76 84 98 78

Is there significance difference across workers and machines? Use ANOVA table

(10 marks)

1. A manufacturer of TV sets was trying to find out what variables influenced the purchase of a TV set. Level of income was suggested as possible variables influencing the purchase of TV Sets. A sample of 500 households was selected and the information obtained is classified as shown below.

Have TV set        Do not have TV set

Low income group                                         0                            250

Middle income group                                   50                          100

High income group                                        80                             20

Is their evidence from the above data of a relationship ownership of TV sets and level of income?                                                                                                                            (10 Marks)