Basic Statistics Model Question

Group A

Attempt any two questions.         [2×10 = 20]

1. There are two popular Cyber Café’s (namely Café A and Café B) in Kathmandu located at Thamel area. Each of them has good number of computers in the cyber and maintains peace, comfort and good working environment. Each costumer, before entering into the café, asks to the café owner about the average time to download an image file since the internet in Kathmandu is a bit of sporadic. Each of them replied that the time to download an image file is on an average no more than 70 seconds. The following is the data of downloading time for an image file experienced by 8 customers in each café in some random 8 different days. 

a) Explain whether the owner’s response to the costumers are satisfied in each café? Even having the average waiting time within the owner’s limit, is there any further comments on the data with reference to measures of central tendency you have computed? Discuss.

b) What similarities and differences are observed based on the average download time in Café A and in café B?

c) Compare the download time between two café’s with respect to variability and shape of the data distribution.

d) On the basis of your statistical analysis, which café would be suggested to the customers so that one can download an image file in a lesser time?

2. A big computer supplier in Kathmandu used to sell large number of computers in each year. His interest is to increase his sales volume in each year for which the supplier has started to take the help of advertisement and allocated some advertisement expenditure in his annual budget each year. The supplier wants to quantify the effect of advertise expenditure on sales of computers. The advertisement expenditure (in lakhs rupees) and their corresponding sales from the computers (in crores rupees) is tabulated as follows.

Assuming that the relationship between the advertisement expenditure and sales is linear. Response the following questions.

a) Perform appropriate statistical analysis and quantify the effect of advertisement on sales obtained from the computer selling. Also interpret the results.

b) Estimate the sales corresponding to advertising expenditure of Rs. 45 lakhs.

3. The following data represent the number of days absent of IT faculty per semester in a population of 4 faculties in an academic institute.

a) Select all possible samples of size n = 2 with replacement, and construct the sampling distribution of mean.

b) Compare the population mean and mean of all sample means. Are they equal?

c) Compare the shape of the population data and shape of the sampling distribution. Do you find any differences? Comment.

d) Compare the population standard deviation and standard deviation of sample means and explain your observation.

Group B

Attempt any eight questions.         [8×5 = 40]

4. Explain the differences between ordinal and interval scales of measurement with suitable examples.

5. The following are the two regression lines: 3X+2Y=26 & 6X+3Y=31 Compute the correlation coefficient between them and interpret the result.

6. Following table represents the probability distribution for the number of computers crashes monthly in a reputed software company in Biratanagar.

Compute mean and standard deviation of number of computer crashes and interpret them.

7. A set of final examination grades in Basic Statistics, is following normal distribution with mean of 73 and standard deviation of 8.

a) What is the probability of a student secured less than 93 marks?

b) What is the probability of a student secured marks between 65 and 89?

8. The rate of denying to take vaccine for COVID19 in a rural population of India is reported to be 0.45 per 10,000 people. If the distribution of denying follows Poisson distribution, what is the probability that in the next 10,000 people, there will be:

a) No one will deny to take vaccine?

b) At least two persons will deny to take vaccine?

9. Suppose Rajesh receives 50 messages and Harish receives 90 messages in the personal emails respectively. Please note that the email address of Rajesh and Harish is different. Rajesh receives 1% junk emails, and Harish receives 2% junk emails. A person is chosen at random at the end of a day and found the email message is junk. What is the probability that this junk email found in the Harish’s email inbox?

10. The standard deviation of a symmetric distribution is 7. Compute the possible value of fourth central moment for the distribution to be (i) mesokurtic (ii) platykurtic, and (iii) leptokurtic.

11. Assuming that the population is normally distributed, construct 95% confidence interval for the population mean using the following sample data. 

Again in the same data set, replace the value of 20 by 6, then compute the confidence interval for the mean. Explain why there is considerable difference in the confidence interval?

12. Write short notes on the following:

        a) Box and whisker plot

        b) Choice of appropriate measure of central tendency