# Business Statistics || Fall 2015 || Pokhara University

 Level:  Bachelor Semester –Fall Year: 2015 Programme: BBA/BBA-BI/BBATT/BCIS Full Marks: 100 Course: Business Statistics Pass Marks: 45 Time:  3hrs.

 Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

Section “A”

Attempt all the questions.

10×2
1. The stem and Leaf display represent the bounced check fee for a sample of 25 banks for direct deposit customers.

Stem       Leaves

1             5  5  8  8

2             0  0  0  0  1  2  2  5  5  5  5  8  8  9

3             4  5  6  7  7

4             1  2

a)       What are the two pieces of information obtained from this stem and leaf display?

2. The coefficient of variations of the two series are 75%and 90% and their standard deviations are 15 and 18 respectively Find their means.
3. Describe the type I and II error.
4. If a random sample of size 36 is drawn from a finite population of 400 units without replacement, then find the standard of the sample mean, if population S.D is 10.
5. What are the sources of data? Write down the methods of collecting primary data.
6. State the necessary conditions to apply binomial distribution.
7. A random variable x has the following probability distribution.

 Values of x:((x) -2 -1 0 1 2 3 Probability: p(x) 0.1 k 0.2 2k 0.3 k

Find the value of k.

8. What is the difference between mutually exclusive and not mutually exclusive expectations? Given an example of each.
9. Differentiate Categorical and numerical variables.
10. Describe the importance of sampling.
Section “B”

Attempt any six questions

6×10

11. A direct undergraduate program on a leading management college affiliated with Pokhara University is interested to know the prior academic performance of the student for new admission. For this, he has compiled the following data of the percentage of plus two examinations of a student who had applied in his college.

 Plus Two percentage Frequency 40-50 3 50-60 39 60-70 35 70-80 6 80-90 1

Construct of giving and answer the following question.

a)       If 80 percent and above is the criteria to get distinction marks, then what percentage of the student applied at that college obtain distinction marks?

b)       If the director set up a benchmark to restrict those students who have obtained less than 55 percent in their plus two examinations referring class occupancy capacity. Then what percentage of the application will be disqualified for admission?

12. a)       Nepal Telecom announced an advertisement for the post of telecommunication engineer to fulfill one vacant post for its Butwal branch. The application of the potential candidates is presented in the following table.

If one of the application is selected at random, find the probabilities that

 Age (years) Bachelor in Engineering (B.E.) Master of Engineering (M.E.) Under 25 60 8 25-30 7 26 Above 30 9 10

i.            He has completed a master in engineering given that he is above 30 years old

ii.            He has done bachelor’s in engineering and he is lies between 25 to 30 years.

b)       Using the information listed below determine Index for Qualitative  (IQV) to find the ecological region-wise diversity for mountains, hills, and Tarai on the basis of the type of school attended by individuals currently in school by percentage.

 Type of School Attended Mountain Hills Tarai Community Government School /College 90.6 74.4 66.1 Institutional /Private School /College 9.3 25.1 31.7 Other School /College 0.1 0.4 2.2 Total 100.0 100.0 100.0

13. a)       An advertising executive is studying television viewing habits of married men and women during prime time hours. On the basis of post-viewing records, the executive has determined that during prime time husband are watching television 60% of the time 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 it. Find the probability that

i.            The wife is watching television in prime time

ii.            If the wife is watching television, the husband is also watching television.

b)       A survey conducted in 2011 found about 40% of the Nepalese workers who have been gone aboard are illegal If in a sample of 7 Nepalese workers who had gone abroad what is the   probability that

i.            Exactly 5 are illegal

ii.            At least 2 are legal.

14. In the final examination of the statistics subject, the marks obtained by students were observed to be normally distributed with a mean of 73 and a standard deviation of 8.

a)       What is the probability of a student getting marks of more than 60?

b)       What percentage of students scored marks between 60 to 90?

c)       Only 5% of the students appearing in the exam score higher than which marks?

15. a)       Population consists of the Fortune 500 Companies (fortune Web site) as ranked by Revenues. You are trying to find out the average Revenues, for the companies on the list. The population standard deviation is \$15,056.37. A random sample of 64 companies obtained a sample mean of \$10,672.87. Given 90% confidence interval estimate for the average revenues.

b)       Two types of drugs were used on 5 and 7 patients for reducing their weight Drugs A were imposed and drug B indigenous. The decrease in the weight after using the drugs for six months was as follows.

 Drug A 12 13 11 10 Drug B 9 12 14 15 10 9 8

Is there a significant difference in the efficiency of the two drugs? It not which drug should you buy?

16. The following are the weekly production in units of 60 workers in a manufacturing company.

 23 35 41 82 75 46 48 88 72 44 85 51 51 77 62 75 68 50 64 25 49 56 55 16 82 39 32 51 52 62 19 52 54 63 45 56 33 48 67 59 40 54 50 64 46 69 57 40 39 49 55 53 20 55 72 57 52 57 42 75

The manager has decided to give a bonus of Rs.5,10,15,20 and 25 to each worker in the respective output group of 40 or over weekly output.

i.            Find the average bonus received by the workers.

ii.            Find S.D, C.V.  bonus.

Section “C”

a.        a.    Mini Case 1

Prior to 2048 economy of Nepal was based on Agricultural GDP. At that time from the Far, Western region farmers exported the Dairy product to India. Nepalese Ghee was highly demanded in major cities of India. Farmers of Kathmandu valley and its surrounding export red chilly and garlic to China. But after the establishment of democracy (after 2047) farmers started migrating from Nepal to the Middle East labor-market and other countries. This caused a heavy decrease in farming. As a result, the agricultural GDP started to fall vertically and non-agricultural GDP increased rapidly.  The following data represents the agricultural and non-agricultural scenario from 2031 to 2063 in Nepal. Do average contributions of Agricultural GDP is higher than Nonagricultural GDP before 2048 and agricultural GDP is lower than nonagricultural GDP after 2048 (including 2048)? Also, find standard deviation and interpret its meaning? Which of the following cluster shows the consistent growth rate if the consistent growth rate is required for a sustainable economy?

 Year Agricultural GDP (in millions) Nonagricultural GDP(in millions) Year Agricultural GDP(in millions) Nonagricultural GDP (in millions) 2048 55368 60759.3 2031/32 11435 4531 2049 65156 79777.1 2032/33 11495 5094 2050 70090 95259.9 2033/34 10389 5866.3 2051 80589 111007 2034/35 11616 6805 2052 85569 124405 2035/36 13365 11327 2053 96896 142492 2036/37 13520 8366 2054 108785 160785 2037/38 15510 9956 2055 112495 177303 2038/39 17715 11322 2056 132373 197645 2039/40 19082 12562 2057 145131 221120 2040/41 22570 14434 2058 151059 242993 2041/42 22761 21680.1 2059 160144 245994.4 2042/43 27136 26078.5 2060 171104 266441.8 2043/44 30623 30517.5 2061 183117 291801.5 2044/45 36755 36415.1 2062 194363 314288 2045/46 42572 43258.6 2063 212828 345042.2 2046/47 50470 49231.8 Sum 2025066.5 3077114.2 357014 297444.9 Sum of Square 292849780145.25 706008683160.60 10197799456 8621513820

b.       Mini Case 2

Green Valley

The green valley assembly company assembles consumer electronic products. For manufacturing that needs temporary extra production capacity. As such, it has periodic product change, because the product green valley assembles is marketed under the label of well-known manufactures, high quality is a must.

Tom Bradley, of the green valley personal department, has been very impressed by recent research concerning job-enrichment programs. In particular, he has been impressed with the increase in quality that seems to be associated with these programs.

However, some studies have shown no significant increase in quality, and they imply that the money spent on such programs has not been worthwhile.

Tom has talked to John the production manager, about instituting a job-enrichment program in the assembly operation at the green valley. John was somewhat pessimistic about the potential, but he agreed to introduce the program. The plan was to implement the program in one wing of the plant and continue with the current method in another wing. The procedure was to be in effect for six months after that period, a test would be made to determine the effectiveness of the job-enrichment program.

After the six month trial period, a random sample of employees from each wing produced the following output measures:

 Old Job- Enrichment n1=50 n2=50 Mean= 11/hr Mean=9.7/hr S.D= a.2/hr S.D=0.9/hr

Both John and Tom wonder whether the job-enrichment program has affected production output. They would like to use these sample results to determine whether the average output has changed and to determine whether the employees’ consistency has been affected by the new program. Based on the above information set the null and alternate hypothesis and test whether the Job-Enrichment program is effective or not use the p-value approach at 3% level of significance.

;2×10

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