Business Statistics || Fall 2017 || Pokhara University

 Level:  Bachelor Semester – Fall Year: 2017 Program: BBA 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. Describe the inferential Statistics briefly.
2. Explain type I and type II errors briefly.
3. Write down the area properties of normal distribution.
4. Define the term, sample space, and an exhaustive number of events.
5. What is a confidence interval? What do you understand by 95% confidence level?
6. The time records of 11 students  to get ready for college is recorded(in minutes) as: 9,  8,  5,  10,  12,  15,  11,  10,  13, 12,  11. Find 3rd quartile and interpret it.
7. A bag contains 4 black and 3 white balls. If two balls are drawn at random, what is the probability that both balls are each color?
8. If the mean and mode of the data are 12 and 14 respectively. Find median.
9. If a random sample of size 36 is drawn from a finite population of 400 units without replacement, then find the standard error of the sample mean, if population S.D is 10.
10. The following data represents the bounced check fee in dollars for a

sample of

23 banks for direct-deposit customers.

26,  28,  20,  20,  21,  22,  25,  25,  18,  25,  15,  20,  18,  20,  25,  25,  22,  30,  30,  30,  15,  20,  29

i)                    Place the data into an ordered array.

ii)                  Set up the stem – and – leaf display for these data.

Section “B”

Attempt any six questions

6×10
11. a)       The records of the sales in a small grocery store for the 360 days that it opened during the year

 Sales,(in\$100s) Below 2 2-3 3-4 4-5 5-6 6-7 7-8 8 and above Number of days 15 27 64 72 86 70 16 10

Days for which sales fall below \$325 are classified as ’poor and those for which the sales exceed \$775 are classified as ‘good’ days in 2002.

i.            Draw less than the cumulative frequency graph.

ii.            Use the graph to estimate the number of poor days.

iii.            Use the graph to estimate the number of good days.

b)      The hourly income of 320 workers of a company are given in the table as:

 income(in Rs) Over 100 Over 120 Over 140 Over 160 Over 180 Over 200 Over220 Over240 No. of workers 320 295 250 190 105 50 20 20

Find:

i.            The lowest income of the top 25% of workers.

ii.            The median income of the workers.

12. a)       The following is the percentage distribution of top caste/ethnic groups for two localities:

 Race/ethnic group % in locality A % in locality B Bramins 98.4 33.5 Chhetry 0.8 – Gurung 0.8 55.1 Shrestha – 11.4 Total 100.0 100.0

Compute IQV in both localities and interpret the results.

b)      The following table shows the survey results regarding the purchase behavior of Force TV and DVD players in the last six months of 300 households.

 Purchased TV Purchased DVD Yes No total Force TV 38 42 80 Not Force TV 70 150 220 total 108 192 300

i.         Compute the marginal and joint probabilities of the data given.

ii.       What is the probability that they purchased a DVD player given that the household purchased a forced TV?

13. a)       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. 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. 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)      An office switchboard receives telephone calls at the average rate of 3 calls per minute on an average. What is the probability of receiving

i.            no call in one-minute interval

ii.            At most 3 calls in a 5-minute interval

14. a)       A statistical analysis of 100 long-distance telephone calls made from the headquarters of the bricks and clicks. Computer corporation indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds.

i.            What percentage of these calls lasted less than 180 seconds?

ii.            What is the length of the calls if only 1% of all Calls are shorter?

b)      A political leader wants to estimate her popularity in a certain locality. A random sample of 600 people was taken and it was found that 280 were her supporters. Estimate the percentage of her supporters in the locality at 95% confidence level. What change would you find in the percentage of supporters if the confidence level was changed to 99%?

15. a)       A manufacturer intends that his electric light bulbs have a life of 1000 hours. He tests a sample of 20 bulbs, drawn at random from a batch, and discovers that the mean life is 990 hours sample standard deviation of 22 hours. Does this signify that the batch is not up to the standard?

b)      Eight sales executive trainees are assigned selling jobs right after their recruitment. After a fortnight they have withdrawn their field duties and given a month’s training for executive sales. Sales executed by them in thousands of rupees  before and after the training, in the same period are listed below:

 Sales before training 23 20 19 18 20 18 21 17 Sales after training 25 25 24 22 23 25 24 21

Do these data indicate that the training has contributed to their

Performance?

16. The following data represents the bounced check fee ( in dollars ) for a

sample of 23 banks for direct-deposit customers who maintain a \$ 100

balance and a monthly service fee ( in dollars ) for direct deposit

customers if their account fall below the minimum required balance of \$

1500 for a sample of 26 banks.

Bounced check fee

26,       28,       20,       20,       21,       22,       25,       25,       18,

25,       15,       20,       20,       25,       25,       22,       30,       30,

30,       15,       20,       29,       18

Monthly service fee

12,       8,         5,         5,         6,         10,       10,       9,

7,         10,       7,         7,         5,         0,         10,       6,

9,         12,       0,         5,         10,       8,            5,         5,

9

a)       List the five-number summary of the bounced check fee and of the monthly service fee.

b)      Construct the box-and-whisker plot of the bounced check fee and the monthly service fee.

c)       What similarities and differences are there in the distribution for the bounced check fee and the monthly service?

17 a)       For overseas flights, an airline has three different choices on its dessert menu- ice-cream, apple pie, and chocolate cake. Based on past experience, the airline feels that each dessert is equally chosen. If a random sample of 90 passengers is selected, what is the probability that:

i.            Exactly 20 will choose ice cream for dessert?

ii.            Less than 20 will choose ice cream for dessert?

b)      The probability that the man will be alive 25 years is 2/3 and the probability that his wife will be alive 25 years 2/3. Find the probability that:

i.            Both will be alive.

ii.            At least one will be alive

18. Section “C”

Case Analysis

Mini Case 1 ( Measurement of players’ performance)

Quantifying individual player contributions’ to a team is an important yet difficult task in all team sports. Usually, there are several indicators available to measure player performances, which are based on different aspects of their contributions to the team. Unfortunately, these indicators are mostly related to each other in a manner that oftentimes causes difficulty in constructing an overall performance measure. The following data represents the score of four batsmen in the current IPL T20 2017. Rank the players according to their average run rate and consistency. Which batsman is more reliable? The team manager of the Mumbai Indians is in dilemma to select a more efficient and reliable player for the upcoming season. If you are the statistical consultant of Mumbai Indians which player would you recommend for the coming season? Why?

 A score of the batsman in seven latest games Virat  Kohli Chris Gayle MS Dhoni Suresh Raina 108 135 120 100 113 118 102 90 78 120 40 80 65 56 35 10 55 50 50 30 50 35 50 113 55 10 10 20

Mini Case 2 (Length of Stay of Chinese and Indian Tourist)

The tourism industry has experienced rapid and continuous growth in the last few years, making it one of the leading industries of the world. Tourism is seen as one of the key contributors to national development. The Nepalese tourism industry should be considered to be one of the most important foundations of national economic development and developed accordingly. So the national planning commission of Nepal set the objective: to contribute to the national economy by developing Nepal as one of the most attractive, scenic, and safe tourism destinations in the world, and to increase the flow of tourists both in quality and quantity through the promotion of tourism at the national and international levels and to distribute the benefits they bring justly. To increase the tourist follow in the country it is necessary to motivate and provide the satisfaction to them. It can be believed that satisfied tourists either revisit the same destination or increase their length of stay or recommend the tourist destination to their friends and relatives. As a result tourism industry will be expanded, which can offer opportunities to generate income for business providers and local communities who are living in the area of tourism sites. In the long run, it has a significant contribution to the National GDP. According to tourism statistics in Nepal 2015, Indian tourists ranked 1 and Chinese tourists ranked 2 (on the basis of tourist arrival in Nepal). There is a dilemma what is the length of stay of Indian and Chinese tourists separately. Some hotel owners of the lakeside Pokhara claimed that the average length of stay of Chinese is higher than the average length of stay of Indians. The manager collects the following information regarding the length of stay of some tourists to solve the dilemma but he is a novice, so he has no idea about hypothesis testing. Help him to solve the problem and suggest to him whether the claim of some hotel owner is valid or not.

 Length of Stay (days) Chinese Indian 4 5 30 5 7 10 30 5 7 2 10 2 2 2 2 2 180 1 4 2 30 2 10 2 5 2 5 2 7 2 7 5 7 5 30 2
20

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