Reference no: EM131204331

1) A factory pays workers on piece rate basis and also a bonus to each worker on the basis of individual output in each quarter.

Output (in units)	70-74	75-79	80-84	85-89	90-94	95-99	100-104
Bonus(Rs)	40	45	50	60	70	80	100

The rate of bonus payable is as follows:

94   83   78   76   88   86   93   80   91   82   89   97   92   84   92   80   85   83   98   103   87   88   88   81   95   86   99   81   87   90   84   97   80   75   93   101   82   82   89   72   85   83   75   72   83   98   77   87   71   80

By suitable classification you are required to find:

a). Average bonus per worker for the quarter, Median bonus and Mode

b). Average output per worker.

2). Calculate Karl Pearson's coefficient of correlation from the following data, using 20 as the working mean for price and 70 as the working mean for demand:

Price:	14	16	17	18	19	20	21	22	23
Demand:	84	78	70	75	66	67	62	58	60

i). Estimate the price when Demand is 80.

ii). Estimate the Demand when Price is 25.

3). From the adult male population of four large cities, random samples of sizes given below were taken and the number of married men and single men recorded. Do the data indicate any significant variations among the cities in the tendency of men to marry.

	A	B	C	D	Total
Married	137	164	152	147	600
Single	32	57	56	35	180
Total	169	221	208	182	780

Given : Chi - square tabulated = 7.82 for 5% LOS and 3 d.f.

4). The demand for a particular spare part in a factory was found to vary from day to day. In a sample study the following information was obtained.

Day	Mon.	Tues.	Wed.	Thurs.	Fri.	Sat.
No. of parts demanded	1124	1125	1110	1120	1126	1115

Test the hypothesis that the number of parts demanded does not depend on the day of the week. [tabulated value of chi-square is = 11.07].

5). A ample analysis of examination results of 500 students was made. It was found that 220 students had failed , 170 had secured a third class, 90 were placed in second class and 20 got first class. Are these figures commensurate with the general examination result which is the ratio of 4 : 3 : 2 : 1 for the various categories respectively. The table value of chi - square for 3 d.f at 5% level of significance is 7.81 .

6). The mean life of a sample of 10 electric light bulbs was found to be 1,456 hours with S.D = 423 hours. A second sample of 17 bulbs chosen from a different batch showed a mean life of 1,280 hours with S.D of 398 hours. Is there a significant difference between the means of the two samples.

Given : t - tabulated = 2.06 for 25 d.f and 5% LOS

7). To verify whether a course in Accounting improved performance , a similar test was given to 12 participants both before and after the course. The original marks - recorded in alphabetical order of the participants were 44 , 40 , 61 , 52 , 32 , 44 , 70 , 41 , 67 , 72 , 53 and 72. After the course the marks were in the same order 53 , 38 , 69 , 57 , 46 , 39 , 73 , 48 , 73 , 74 , 60 and 78. Was the course useful? [ Given : t - tabulate for 5 % LOS and d.f = 11 is 2.201 ].