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 ].