POKHARA UNIVERSITY

Level: Bachelor                                  Semester: Spring                                   Year: 2023

Programme: BBA/BI/TT/BCIS/BHCM/BHM                                              Full Marks: 100

Course: Business Statistics                                                                     Pass Marks: 45

Time: 3 hrs. 

                                                          Section "A"

                                               Very Short Answer Questions

Attempt all the questions. [10×2] 

1. What are the important scopes of statistics in the business sector?

2. Prepare stem and display from the following data. What percentage of items is before 6.1?

   3.5,4.3,4.8,4.8,4.9,5.4,5.5,5.5,5.9,6.1,6.3,6.6,7.3,8.5

3. Write short notes on a five number summary.

4. In a single throw of two dice, what is the probability of getting a total sum of 8 or 9.

5. Write any two characteristics of the binomial distribution.

6. Find out class intervals from the following frequency distribution.

             Mid-point              5       10      15     20     25      30

             Frequency             1       3        5     10       2        1

7. The average daily income for a group of 50 persons in a factory was calculated to be Rs.169. It was later discovered that one figure was misread as 134 instead of the correct value 143, Calculate the correct average income.

8. Define statistics and parameters.

 9. Discuss type I and type II errors briefly.

10. A random sample of 50 employees of a factory shows sample mean earning of Rs. 55000 and standard error of sample mean is found to be Rs. 750. Construct 95% confident interval for mean earning of all employees in a factory.

                                                             Section "B"

                                            Descriptive Answer Questions

Attempt any six questions. [6×10]

11. a) What do you mean by secondary data? Discuss its advantages and disadvantages.

      b) Locate the median after drawing the less than and more than ogives for the following distribution: 

Marks	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No.of Students	7	11	24	32	9	14	2	1

12. a) 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

i.  What percentage of item is before 30,

ii. Construct the relative percentage frequency distribution. 

b) The record of 300 lecturer in Pokhara University are given below:

Age (yrs)	Master’s degree	M.Phil degree	Ph. D. degree	Total
Under 35   35-45   Over 45	50   60   80	20   30   25	5   10   20	75   100   125
Total	190	75	35	300

If a lecturer is selected at random, find the probability that.

i. He has a Ph. D. degree

ii. He is over 45 or Ph.D.

iii. He has an M. Phil degree given that he is under 35 years.

13.a) A multiple choice test has 5 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly. What is the probability that he will get

 (i) five questions correct? 

(ii) at least three questions correct? 

b) In a certain factory. Machines I, II and III are all producing springs of the same length. Of their production, machines I, II and III produce 2%, 1% and 3% defective springs respectively. Of the total production of springs in the factory, machine I produces 35%, machine II produces 25%, and machine III produces 40%. If one spring is selected at random from the total springs produced in a day, find

 (i) the probability that it is defective

(ii) the conditional probability that it was produced by machine III. 

14. a) If 3% of the bulbs manufactured by a company are defective, find the probability that in a sample of 100 bulbs

 (i) none is defective         (ii) at least 2 bulbs will be defective.

b) A batch of 5000 electric lamps has a mean life of 1000 hours and standard deviation of 75 hours. Assuming normal distribution, 

(i) what percentage of lamps will fail before 925 hours?

(ii) how many lamps will fail between 950 and 1000 hours?

15. a) Mr. Dinesh, a noted economist, surveyed 550 households in a particular place and found that 150 of them were under the poverty level. Set up a 99% confidence limit for the proportion of households under the poverty level.

b) An experiment was run to determine the effect of a new type of drug on blood pressure, the person has their blood pressure measured after the drug is given. The result of experiment are as follows:

Person	1	2	3	4	5	6	7	8	9	10
Before	116	118	120	124	128	130	131	134	136	137
After	119	124	126	128	121	135	137	138	139	135

Test the hypothesis that new drugs raise blood pressure at a=0.05.(a=alpha)

16.a) A person is interested in computing the average monthly salary of employees of NTC. He took a random sample of 400 employees and found that the average salary was Rs. 30,000 with standard deviation as Rs. 5,000. Calculate the 95% confidence interval for the average salary for all the employees of NTC.

b) Compute five number summary of the following data and plot box-and-whisker plot. Also determine the shape of the distribution.

    27,25, 20, 15, 30, 34, 28, 25

17.a) There are 3 economists, 4 engineers, 2 statisticians and 1 doctor. A committee of 4 from them is to be formed. Find the probability that the committee

i. consists one of each kind

ii. has at least one economist

iii. has the doctor as a member and three others

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

Type of school Attended	Mountain	Hills	Terai
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

                                                                  Section "C"

                                                               Case Analysis 

18. A large retail chain in Kathmandu wanted to know if there was a significant difference between the level of inventory kept by its stores that are able to order online through the Internet with the distribution Centre and those that must use FAX. The headquarters of the chain collected the following sample data from 12 stores that used direct FAX and 13 that used Internet connections for the same non-perishable items in terms of the number of days' coverage of inventory: For example, the first value for a store using FAX has a value of 14. This means that the store has on average 14 days' supply of products to satisfy estimated sales until the next delivery arrives from the distribution Centre.

Stores Fax	14	11	13	14	15	11	15	17	16	14	22	16
Stores Internet	12		14	11			15			22	19		4

a) Compare mean and median of number of days' coverage of inventory between two stores. [2]

b) Which store has consistency in terms of covering inventory levels?  [3]

c) Prepare box and whisker plot for the stores that use FAX and comment on the shape of distribution. [5]

d) Construct 95% confidence interval estimate for number of days' coverage of inventory. [5]

e) Indicate appropriate null and alternative hypotheses for this situation if we wanted to show if those stores ordering by FAX kept a higher inventory level than those that used Internet. Using the critical value method, at a 1% significance level, does this data indicate that those stores using FAX keep a higher level of Inventory than those using Internet?  [5]