Business Statistics Sample Assignment
SECTION A (COMPULSORY)
Answer ALL questions from this Section.
QUESTION 1 (25 Marks)
XYZ, a retail store, operates in a highly competitive market with many competitors. The manager has been tasked to do some statistical analysis on the monthly expenses over the last five years. Table 1.1 shows the data that was collected.
Monthly Expenses (S$) 
Frequency 
0 and less than 150 
5 
150 and less than 300 
8 
300 and less than 450 
15 
450 and less than 600 
9 
600 and less than 750 
17 
750 and less than 900 
6 
Total 
60 
Table 1.1
(a) For the above grouped data, calculate:
(i) Mean 482.50 (2 marks)
(ii) Median 483.33 (2 marks)
(iii) Mode 663.16 (2 marks)
(iv) Sample variance 48,883.47 (3 marks)
(v) Coefficient of Variation 45.82% (3 marks)
(b) Explain with the aid of a diagram, the skewness of the monthly expenses distribution. Left Skewed (3 marks)
(c) Which measure of central tendency (mean, median or mode) would you choose for the above grouped data? Explain. median (3 marks)
(d) If 80% of the monthly expenses is below $600, then it indicates that
the XYZ has not been overspending. From the above grouped data, would you
say that XYZ has been overspending? Show your calculation. XYZ has been overspending (3 marks)
(e) The manager wants to do a competitorsâ€™ analysis from two of their closest competitors.
Statistical Measure 
Competitorsâ€™ Monthly Expenses 

Competitor A 
Competitor B 

Mean 
430 
450 
Median 
450 
430 
Mode 
420 
470 
Standard Deviation 
200 
250 
Table 1.2
Using the information in Table 1.2, compare XYZ Company with competitor A and competitor B, comment on the following:
(i) Which company has the most variation? Explain. B (3 marks)
(ii) The manager of XYZ Company made the following statement, â€śCompetitor A spends on the average the most amount of money in the past 5 years in the industry.â€ť Is this an Inferential Statistics or a Descriptive Statistics? (1 mark)
Inferential Statistics
QUESTION 2 (25 Marks)
(a) A sample of 500 respondents was surveyed in a large suburban area to determine various information concerning consumer behaviour. Table 2.1 shows the information obtained.
Male 
Female 

Enjoys shopping for clothes 
136 
224 
Does not enjoy shopping for clothes 
104 
36 
Table 2.1
(i) Compute the probability that a respondent is a female and enjoys shopping for clothes. 0.448 (2 marks)
(ii) What is the probability that a respondent chosen enjoys shopping for clothing given that the respondent is a female? 0.8615 (3 marks)
(iii) Are the categories of â€śEnjoys shopping for clothingâ€ť and â€śFemaleâ€ť statistically independent events? Explain your answer. No (5 marks)
(b) A building contractor claims that he is able to renovate a five room HDB flat in mean time of 40 days with a standard deviation of 5 days. Assume from past experience, that the days to complete similar flats are normally distributed with mean and standard deviation as estimated above.
(i) What proportion of five room HDB flats will be completed in less than 35 days? 0.1587 (2 marks)
(ii) What proportion of five room HDB flats will be completed in between 28 and 32 days? 0.0466 (3 marks)
(iii) What is the minimum number of days to complete the renovation for the slowest 10% of five room HDB flats? 46.4 days (4 marks)
(c) An advertising executive is studying television viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 60% of the time. It has also been determined that when the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 30% of the time the wife is watching television. Find the probability that
(i) the wife is watching television during prime time hours. 0.36 (2 marks)
(ii) if the wife is watching television, the husband is also watching television.
0.667 (4 marks)
SECTION B
Answer any TWO questions from this Section.
QUESTION 3 (25 Marks)
A manager of a bank claims that 80% of their customers use the ATM machine at least once a month to withdraw cash. The average amount withdrawn by these customers is $1,000 with a standard deviation of $10.
The average amount withdrawn by the remaining 20% customers is $200 with a standard deviation of $5. The maximum number of customers using the ATM machine was found to be 200. A random sample of 36 customers was selected.
(a) Identify the variable(s) for the above and state the type and level of measurement for the variable(s) identified. (4 marks)
(b) What is the probability that in a random sample of 5 customers, 80% will use the ATM machine at least once a month? 0.4096 (3 marks)
(c) What is the probability that in a random sample of 5 customers, at least 80% will use the ATM machine at least once a month? What assumption is necessary for the distribution? 0.7373 (5 marks)
(d) Calculate the average amount of cash per withdrawal. $840 (3 marks)
(e) Calculate the probability that the amount withdrawn by a customer is at most $845. 0.7123 (4 marks)
(f) Calculate the probability that the average amount withdrawn by a customer is at most $842. 0.9292 (4 marks)
(g) Calculate the probability that the average withdrawn by a customer is at least $840. 0.5 (2 marks)
QUESTION 4 (25 Marks)
A sales manager wants to find out the relationship between the amount his shop spends on advertisements and the sales revenue. He took note of his spending on advertisements and sales revenue earned for the past 7 months.
X, Amount spent on Advertisements (S$â€™000) 
Y, Sales Revenue (S$â€™0000) 
230 
152 
143 
78 
177 
90 
259 
142 
374 
150 
132 
79 
265 
151 
Table 4.1
(a) Determine and interpret the regression line. = 39.2543 + 0.3590X (10 marks)
(b) Calculate and interpret the correlation coefficient. 0.8442 (5 marks)
(c) Estimate the amount of sales revenue if his shop spends $140,050 on advertisements. $895,322.50 (2 marks)
(d) The sales manager realised that he made a wrong calculation on the sales revenue amount. All sales revenue amount should decrease by $10,000. Without any further calculations, state any change expected on the regression coefficients. (4 marks)
a will decrease by 1, no change to b
(e) Discuss and comment on the accuracy of the following statements made by the manager after conducting the correlation and regression analysis:
(i) â€śAdvertising causes our sales revenue to increase!â€ť (2 marks)
(ii) â€śOur sales revenue is only affected by the change in advertising costs!â€ť
(2 marks)
See lecture notes
QUESTION 5 (25 Marks)
The Body Mass Index (BMI) is a measure for human body shape based on an individual's weight and height. It is a standardised estimate of an individualâ€™s relative body fat calculated from his or her height and weight. You took the measurement of BMI for 25 men and 25 women from the School of Business and Accountancy and calculated the following statistics in Table 5.1.
Gender 
Mean 
Variance 
Women 
25 
36 
Men 
26 
9 
Table 5.1
The upper limit for a normal BMI for an adult is 23. You may assume that the level of significance is 5%.
(a) Based on the above information, can you say that either the group of women or group of men have above normal BMIs? Explain. (6 marks)
Female: (22.5232, 27.4768)
Male: ( 24.7616, 27.2384 )
(b) Construct the hypothesis test statements for part (a). Briefly explain the construction in Singapore context. Ho: Âµ â‰¤ 23 grams Ha: Âµ > 23 grams (6 marks)
(c) What is the critical value when testing the hypothesis? 1.711 (3 marks)
(d) What are the limits of the acceptance region when testing the hypothesis? (4 marks)
Female: 27.0532
Male: 27.0266
(e) What is the standardised value of the sample mean for both gender? (2 marks)
Female: 1.667
Male: 5.00
(f) Do the sample results provide sufficient evidence to indicate that the mean BMI for an adult is above normal? You are required to explain for both genders. (4 marks)
BMI_{W} for women is not significantly greater than average
BMI_{M} for men is significantly greater than averageStandard Normal Distribution
Z 
.00 
.01 
.02 
.03 
.04 
.05 
.06 
.07 
.08 
.09 
0.0 
.0000 
.0040 
.0080 
.0120 
.0160 
.0199 
.0239 
.0279 
.0319 
.0359 
0.1 
.0398 
.0438 
.0478 
.0517 
.0557 
.0596 
.0636 
.0675 
.0714 
.0753 
0.2 
.0793 
.0832 
.0871 
.0910 
.0948 
.0987 
.1026 
.1064 
.1103 
.1141 
0.3 
.1179 
.1217 
.1255 
.1293 
.1331 
.1368 
.1406 
.1443 
.1480 
.1517 
0.4 
.1554 
.1591 
.1628 
.1664 
.1700 
.1736 
.1772 
.1808 
.1844 
.1879 
0.5 
.1915 
.1950 
.1985 
.2019 
.2054 
.2088 
.2123 
.2157 
.2190 
.2224 
0.6 
.2257 
.2291 
.2324 
.2357 
.2389 
.2422 
.2454 
.2486 
.2517 
.2549 
0.7 
.2580 
.2611 
.2642 
.2673 
.2704 
.2734 
.2764 
.2794 
.2823 
.2852 
0.8 
.2881 
.2910 
.2939 
.2967 
.2995 
.3023 
.3051 
.3078 
.3106 
.3133 
0.9 
.3159 
.3186 
.3212 
.3238 
.3264 
.3289 
.3315 
.3340 
.3365 
.3389 
1.0 
.3413 
.3438 
.3461 
.3485 
.3508 
.3531 
.3554 
.3577 
.3599 
.3621 
1.1 
.3643 
.3665 
.3686 
.3708 
.3729 
.3749 
.3770 
.3790 
.3810 
.3830 
1.2 
.3849 
.3869 
.3888 
.3907 
.3925 
.3944 
.3962 
.3980 
.3997 
.4015 
1.3 
.4032 
.4049 
.4066 
.4082 
.4099 
.4115 
.4131 
.4147 
.4162 
.4177 
1.4 
.4192 
.4207 
.4222 
.4236 
.4251 
.4265 
.4279 
.4292 
.4306 
.4319 
1.5 
.4332 
.4345 
.4357 
.4370 
.4382 
.4394 
.4406 
.4418 
.4429 
.4441 
1.6 
.4452 
.4463 
.4474 
.4484 
.4495 
.4505 
.4515 
.4525 
.4535 
.4545 
1.7 
.4554 
.4564 
.4573 
.4582 
.4591 
.4599 
.4608 
.4616 
.4625 
.4633 
1.8 
.4641 
.4649 
.4656 
.4664 
.4671 
.4678 
.4686 
.4693 
.4699 
.4706 
1.9 
.4713 
.4719 
.4726 
.4732 
.4738 
.4744 
.4750 
.4756 
.4761 
.4767 
2.0 
.4772 
.4778 
.4783 
.4788 
.4793 
.4798 
.4803 
.4808 
.4812 
.4817 
2.1 
.4821 
.4826 
.4830 
.4834 
.4838 
.4842 
.4846 
.4850 
.4854 
.4857 
2.2 
.4861 
.4864 
.4868 
.4871 
.4875 
.4878 
.4881 
.4884 
.4887 
.4890 
2.3 
.4893 
.4896 
.4898 
.4901 
.4904 
.4906 
.4909 
.4911 
.4913 
.4916 
2.4 
.4918 
.4920 
.4922 
.4925 
.4927 
.4929 
.4931 
.4932 
.4934 
.4936 
2.5 
.4938 
.4940 
.4941 
.4943 
.4945 
.4946 
.4948 
.4949 
.4951 
.4952 
2.6 
.4953 
.4955 
.4956 
.4957 
.4959 
.4960 
.4961 
.4962 
.4963 
.4964 
2.7 
.4965 
.4966 
.4967 
.4968 
.4969 
.4970 
.4971 
.4972 
.4973 
.4974 
2.8 
.4974 
.4975 
.4976 
.4977 
.4977 
.4978 
.4979 
.4979 
.4980 
.4981 
2.9 
.4981 
.4982 
.4982 
.4983 
.4984 
.4984 
.4985 
.4985 
.4986 
.4986 
3.0 
.4987 
.4987 
.4987 
.4988 
.4988 
.4989 
.4989 
.4989 
.4990 
.4990 
3.1 
.4990 
.4991 
.4991 
.4991 
.4992 
.4992 
.4992 
.4992 
.4993 
.4993 
3.2 
.4993 
.4993 
.4994 
.4994 
.4994 
.4994 
.4994 
.4995 
.4995 
.4995 
3.3 
.4995 
.4995 
.4995 
.4996 
.4996 
.4996 
.4996 
.4996 
.4996 
.4997 
3.4 
.4997 
.4997 
.4997 
.4997 
.4997 
.4997 
.4997 
.4997 
.4997 
.4998 
3.5 
.4998 
.4998 
.4998 
.4998 
.4998 
.4998 
.4998 
.4998 
.4998 
.4998 
3.6 
.4998 
.4998 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
3.7 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
3.8 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
.4999 
3.9 
.5000 
.5000 
.5000 
.5000 
.5000 
.5000 
.5000 
.5000 
.5000 
.5000 
Righttailed test a 
Student's t Distribution
Lefttailed test a 
1  a 
Twotailed test a 
Appendix 3 
Student's t Distribution 
degrees of freedom 
Confidence Level ( 1  a ) 

0.80 
0.90 
0.95 
0.98 
0.99 
0.999 

Level of Significance for OneTailed Test ( a ) 

0.10 
0.05 
0.025 
0.01 
0.005 
0.0005 

Level of Significance for TwoTailed Test ( a ) 

0.20 
0.10 
0.05 
0.02 
0.01 
0.001 

1 
3.078 
6.314 
12.706 
31.821 
63.657 
636.619 
2 
1.886 
2.920 
4.303 
6.965 
9.925 
31.599 
3 
1.638 
2.353 
3.182 
4.541 
5.841 
12.924 
4 
1.533 
2.132 
2.776 
3.747 
4.604 
8.610 
5 
1.476 
2.015 
2.571 
3.365 
4.032 
6.869 
6 
1.440 
1.943 
2.447 
3.143 
3.707 
5.959 
7 
1.415 
1.895 
2.365 
2.998 
3.499 
5.408 
8 
1.397 
1.860 
2.306 
2.896 
3.355 
5.041 
9 
1.383 
1.833 
2.262 
2.821 
3.250 
4.781 
10 
1.372 
1.812 
2.228 
2.764 
3.169 
4.587 
11 
1.363 
1.796 
2.201 
2.718 
3.106 
4.437 
12 
1.356 
1.782 
2.179 
2.681 
3.055 
4.318 
13 
1.350 
1.771 
2.160 
2.650 
3.012 
4.221 
14 
1.345 
1.761 
2.145 
2.624 
2.977 
4.140 
15 
1.341 
1.753 
2.131 
2.602 
2.947 
4.073 
16 
1.337 
1.746 
2.210 
2.583 
2.921 
4.015 
17 
1.333 
1.740 
2.110 
2.567 
2.898 
3.965 
18 
1.330 
1.734 
2.101 
2.552 
2.878 
3.922 
19 
1.328 
1.729 
2.093 
2.539 
2.861 
3.883 
20 
1.325 
1.725 
2.086 
2.528 
2.845 
3.850 
21 
1.323 
1.721 
2.080 
2.518 
2.831 
3.819 
22 
1.321 
1.717 
2.074 
2.508 
2.819 
3.792 
23 
1.319 
1.714 
2.069 
2.500 
2.807 
3.768 
24 
1.318 
1.711 
2.064 
2.492 
2.797 
3.745 
25 
1.316 
1.708 
2.060 
2.485 
2.787 
3.725 
26 
1.315 
1.706 
2.056 
2.479 
2.799 
3.707 
27 
1.314 
1.703 
2.052 
2.473 
2.771 
3.690 
28 
1.313 
1.701 
2.048 
2.467 
2.763 
3.674 
29 
1.311 
1.699 
2.045 
2.462 
2.756 
3.659 
30 
1.310 
1.697 
2.042 
2.457 
2.750 
3.646 
40 
1.303 
1.684 
2.021 
2.423 
2.704 
3.551 
60 
1.296 
1.671 
2.000 
2.390 
2.660 
3.460 
120 
1.289 
1.658 
1.980 
2.358 
2.617 
3.373 
Âµ 
1.282 
1.645 
1.960 
2.326 
2.576 
3.291 
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