Questions:

1. The General Manager of a large hotel in Bombay wishes to know whether or not the personal

services provided to its customers are uniform throughout the hotel industry. Whether the

clients in the less expensive rooms get the same service as that of clients of more expensive

rooms. The data collected from the comment cards is tabulated below:

Room Charge

RatingRs

50

Rs

100

Rs

150

Rs

200

Excellent 10 25 28 28

Good 24 30 16 16

Average 80 82 21 I3

Poor 40 41 18 25

Were the customers treated differently according to their room charges? Test the hypothesis

at = 0.05 level of significance.

2. The following data was compiled by a researcher studying the role stress and its implications

on personal life in respect of suicides by executives. The data relates to 30 firms over the

three year period:

Number of Suicides

during the Year 0 1 2 3 4 5 6 7 8 9

Observed Frequency 8 18 19 20 16 12 8 4 3 2

Fit a suitable distribution and test its goodness of fit. Use a Kolmogorov-Smirnov test to see

if the fit is ok.

1

3. A Manufacturer of machine parts is considering buying one of 5 machines currently in the

market. The following is the daily output on five randomly selected days for each machine.

Machine 1 Machine 2 Machine 3 Machine 4 Machine 5

72

56

68

65

60

62

70

66

64

78

68

72

74

70

66

64

72

68

68

58

72

62

68

64

70

Do the five machines have equal output rate?

4. The following table gives the yearly sales (in thousand rupees) of a firm in three territories

by its four salesmen.

Salesman

Territory S1 S2 S3 S4

A 10 9 8 14

B 15 16 10 16

C 18 12 11 15

Test whether the difference between the sales affected by four salesmen and the

difference between sales in the three territories are significant.

2

5. The following are the consumer responses for their preference on a four point scale in respect

of two brands of toothpastes for the freshness they provide.

Consumer Number Score for Brand X Score for Brand Y

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

4

2

3

3

4

3

4

1

2

3

2

3

4

3

2

1

2

3

4

3

4

1

1

1

2

3

4

1

3

2

2

1

3

3

1

3

2

4

3

1

3

3

2

2

2

1

3

2

4

3

Will you conclude that the effectiveness of the two brands is the same?

3

6. The data related to mean life times of two brands of machines is given below. The data is based on

the past experience of the users of the machines.

Machine X: 400, 450, 425, 430, 445, 460, 475, 420, 410, 415, 435

Machine Y: 525, 500, 435, 440, 455, 465, 505, 515, 505, 395, 418

Using a suitable test, will you conclude that lifetimes of two brands are equal?

7. A manufacturer of food products uses a machine to insert randomly one of the two types of gifts in

each box. The manufacturer wants randomness so that every purchaser in the neighbourhood does

not get the same gift. A sample of 60 successive boxes was chosen to see if the machine is properly

mixing the two types of gifts. Using the symbol X and Y for gifts, the examination of 60 boxes

revealed the data on gifts as follows:

Y Y X Y Y X X X Y Y X X Y X Y Y Y X X X

X X Y Y X X X Y Y Y Y X Y X X X Y Y Y X

Y Y Y X X Y Y X X X Y Y X X Y X Y Y X X

Using a suitable test, what will you conclude about the randomness?

8. A sample of 400 people were asked their preferences for four brands of tea. 175 preferred

brand A, 120 preferred brand B, 80 preferred brand C and 25 preferred brand D. Does

this indicate a preference?

4

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