Course: Business Statistics

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Course: Business Statistics

Internal Assignment Applicable for April 2020 Examination

Mfr 1 - life of bulf (in hrs)	Mfr 2 - life of bulf (in hrs)
684	819
831	907
859	952
893	994
922	1016
939	1038
972	1096
1016	1153
697	836
835	912
860	959
899	1004
924	1018
943	1072
977	1100
1041	1154
720	888
848	918
868	962
905	1005

1. A sample of 20 bulbs each was picked from the manufacturing facility of two bulb manufacturers – Mfr 1 and Mfr 2. The table above provides the life of bulbs for the two manufacturers. You are a quality testing person and are presented with this data:

i. Which manufacturer has better performance on the life of bulbs? What are the different measures you can consider to calculate performance?

ii. How would you assess the variability in performance of the two bulb manufacturers?

iii. Would your answer to the first question change based on your assessment of the variability in performance of bulb manufacturers?

Answer: (i) To measure the performance of bulbs in terms of life, we need to calculate the arithmetic mean and median and decide accordingly.

Calculation of mean:

Mean:

Answer: (ii) To assess the variability in performance, we can calculate standard deviation and make the decision accordingly.

Calculation of standard deviation

Answer: (iii) As per the first solution (Mean and median) Mfr 2 is better as compared to Mfr 1. Standard deviation is a mathematical tool to help us assess how far the values are spread above and below the mean. A high standard deviation shows that the data is widely spread (less reliable) and a low standard deviation shows that the data are clustered closely around the mean (more reliable). By this also, Mfr 2 is better so there is no change in the solution and it would remain the same.

Question: 2. For the data in the table below:

i. What do the correlation coefficients of 1, shaded in yellow, indicate?

ii. The highest correlation coefficient is 0.84, shaded in green. What can you infer from that score about the relationship between the two variables?

iii. The two lowest correlation coefficients are 0.06 and -0.06. What can you infer from that score about the relationship between the two variables?

r correlation coefficient	Assets	Expense Ratio	Return 2006	3-Year Return	5-Year Return
Assets	1
Expense Ratio	-0.29	1.00
Return	0.08	-0.13	1.00
3-Year Return	0.07	-0.11	0.70	1.00
5-Year Return	0.06	-0.06	0.59	0.84	1.00

Answer: Correlation

When two or more variables move in sympathy with other, then they are said to be correlated. If both variables move in the same direction then they are said to be positively correlated. If the variables move in opposite direction then they are said to be negatively correlated. If they move haphazardly then there is no correlation between them. Correlation analysis deals with the following.

Question (i). What do the correlation coefficients of 1, shaded in yellow, indicate?

A correlation coefficient of 1

Question (ii). The highest correlation coefficient is 0.84, shaded in green. What can you infer from that score about the relationship between the two variables?

Question (iii). The two lowest correlation coefficients are 0.06 and -0.06. What can you infer from that score about the relationship between the two variables?

A negative correlation coefficient of -0.06 means that for every positive increase in one variable, there is

Question 3. The Indian cricket team is visiting New Zealand to play a test series comprising five matches. In each match, assume that the Indian team has a 70% chance of winning. Further, assuming that the matches are independent of each other, what is the probability that:

a. The Indian team will win the series?

Answer: There are 5 matches

Therefore, n = 5

b. The team will win all five matches, and that the team will lose all?

Answer : Team will win all five matches means, n = 5

and team will lose all means, n = 0

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