Business Data Analysis

2372 words - 10 pages

1. Suppose we are interested to estimate the proportion (p) of smokers among the male students in IIMA. Suppose a sample of size 100 is chosen out of the male students and the sample proportion of smokers is found to be 0.2. Give an interval based on your data so that you are 95% confident that the true value of the unknown proportion lies inside it.
How would you explain 95% confidence to a layman? Suppose a professor of IIMA thinks that true proportion is 0.3. Are you ready to accept the professor’s perception based on your data at 99% confidence level?

Solution – 1
Sample Size n = 100 (male smokers)
p = 0.2
Sd (P) = √(pq / n)
= .04
95% confidence interval of p
= ...view middle of the document...

Sd (p) = √(pq / n) = 0.004999

95% confidence interval of p
= 0.51 ± 2 x 0.004999
= 0.5 to 0.52

Since 0.51 lies in the interval 0.5 to 0.52 we can claim with 95% confidence that democrats would win.

At 99 % confidence interval
= 0.51 ± 2.58 x .0049
= 0.49 to 0.52

Since 0.51 lies in the interval 0.49 to 0.52 we can claim with 99% confidence also that democrats would win.

3. A company likes to predict what proportion of people who click on its ad on the web would eventually buy its product. Last month’s data show that 1 million clicked on the ad but 10,000 customers eventually bought the product. Could the company claim with 95% confidence that at least 0.5% of those who clicked would buy its product? How would you explain 95% confidence to a layman?

Solution – 3
Sample Size = 1,000,000
p = 10,000/1,000,000 = .01
Sd (p) = √(pq / n)
= 9.95 x10^(-5)
95% confidence interval of p
= 0.01± 2 x 9.95 x10^(-5)
= .0098 to 0.0102

As 0.5% (.05) does not lie in this interval, the company cannot claim with 95% confidence that at least 0.5% of those who clicked the ad would buy eventually buy the product.

Explanation to a Layman: If one took a sample of no of persons who clicked the advertisement of the Company and whether they bought the product or not then based on the last month’s data ratio / or of a chosen sample of ads clicked to product purchase, we can conclude with 95% confidence that of the sample 0.5% (in the present case) of people may not eventually buy the product.

4. A Call Center is interested to compare the skills of two of its employees, say, Ram and Shyam, in generating subscription to a credit card. It was found during the last month Ram called up 2000 people and 150 of them subscribed while for Shyam the numbers are 1500 and 200. Using the above data could you claim with 95% confidence that Shyam is more competent (in the sense that if Shyam calls up a person, the chance of his/her to subscribe is more than that of Ram)?

Solution – 4
Case – 1: Ram
Total Subscribed 150
Sample size 2000
(No of Persons Called)
p = sample proportion
Sample proportion = 150/2000 = 0.075

95% confidence interval of p
Sd (p) = √(pq / n) =.0059
= 0.075 ± 2 x 0.0059
0.063 to 0.086

With 95 % confidence interval the true value of p (0.075) for Ram’s case lies between 0.063 to 0.086

Case – 2: Shyam
Total Subscribed 200
Sample size 1500
(No of Persons Called)
p = sample proportion
Sample proportion 0.1333

95% confidence interval of p
Sd (p ) = √(pq / n)
= 0.1333 ± 2 x 0.0088
=0.115 to 0.151

With 95 % confidence interval the true value of p (0.133) in Shyam’s case lies between 0.115 to 0.151.
Thus based on past month’s data we can conclude since Shyam’s success ratio is higher in conversion of calling the person to credit card subscription we can conclude with 95% confidence that Shyam is more competent than...

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