MBA in Management Statistics for Managers Final Exam

 

STUDENTS ARE REQUIRED TO ANSWER ALL QUESTIONS 

1.      Samples of light bulbs were obtained from two suppliers and tested ‘to destruction’ in the laboratory. The following results were obtained for the length of life:

	Length of Life (hours)
	700-899	900-1099	1100-1299	1300-1499	Total
Supplier A	14	16	26	12	68
Supplier B	5	36	21	5	67

 

(a)    Which supplier’s bulbs have greater average length of life?

(b)   Which supplier’s bulbs are more uniform in quality?

(c)    Which supplier would you prefer to use

2.      At the end of an MBA course in business statistics, the final examination grades have a mean of 70.2 and a standard deviation of 12.3. There were 210 students on the course. Assuming that the distribution of these grades (all whole numbers) in normal, find:

(a)    the percentage of grades that should exceed 90;

(b)   the percentage of grades less than 35

(c)    the number of failures (pass = 70 per cent)

(d)   the lowest distinction mark if at most the highest 5 per cent of grades are to be awarded distinctions.

3.      Jonida Martinez, researcher for the Colombian Coffee Corporation is interested in determining the rate of coffee usage per household in the United Sates.  She believes that yearly consumption per household is normally distributed with an unknown mean and a standard deviation of about 2 pounds.

a)        If

Martinez

takes a sample of 16 households and records their consumption of coffee for one year, what is the probability that the sample mean is within one pound of the population mean?

b)        How large a sample must she take in order to be 98 percent certain that the sample mean is within one pound of the population mean?

4.      A chain of department stores is moving into a phase of expansion and opening several new stores. As part of the expansion planning process a project team is carrying out an investigation to find out how the sales levels at new stores might be predicted. One approach has been to use regression analysis. The average level of sales per week (y) for each existing store in the chain (fourteen department stores) together with a measure of disposable income per family in each store’s catchment area are given in Table 11.1

Table 11.1

Store number	Average sales per week (₤000s) Y	Average disposable family income (coded) x
1	90	301
2	97	267
3	86	397
4	84	227
5	82	273
6	80	253
7	78	203
8	75	263
9	70	190
10	68	212
11	64	157
12	61	141
13	58	119
14	52	133
Mean	74	217

 

The computer gives the following results after regressing sales against family income:

Variable                       Coefficient

Income             0.17846

Constant           35.228

Correlations Coefficient = 0.92

Standard error = 4.72

 

(a)         According to the above table, what is the predictable average sales per week with average family disposable income at 221?

(b)        How good is the application of regression analysis in the above data?

(c)         What are the limitation of this method to predict the average sales per week?

5.      Factory A conducted a sample check of total number of apples per crate and get the following results.  The Quality Manager would like to see if the data are out of control.

Sample 1	Sample 2	Sample 3	Sample 4	Sample 5
110	93	99	98	109
103	95	109	95	98
97	110	90	97	100
96	102	105	90	96
105	110	109	93	98
110	91	104	91	101
100	96	104	93	96
93	90	110	109	105
90	105	109	90	108
103	93	93	99	96
97	97	104	103	92
103	100	91	103	105
90	101	96	104	108
97	106	97	105	96
99	94	96	98	90
106	93	104	93	99
90	95	98	109	110
96	96	108	97	103
109	96	91	98	109
90	95	94	107	99
91	101	96	96	109
108	97	101	103	94
96	97	106	96	98
101	107	104	109	104
96	91	96	91	105

(a)        Calculate LCL & UCL

(b)        Calculate Average of Mean

(c)        Draw the X – R chart

This is the End of the Exam Paper