Advanced Statistics. Q1. Bajaj Auto is a global two-wheeler & three-wheeler manufacturing company in India. The production manager of the two-wheeler division of the company is not happy these days. She is worried about the high degree of variability in the daily output of employees. This high degree of variability (which worked out to be 60 units for long period of time) actually hampers proper planning as production can not happen at a constant rate. In order to reduce the variability, the manager figured out a new plan which involved staggering shifts and this new plan has now been in operation for full 5 weeks. A random sample of 10 workers has shown the following output:
78, 84, 53, 66, 81, 61, 52, 80, 85, 69
Taking level of significance as 0.05:
i) Formulate Hypothesis
ii) Is it a one-tailed test or a two-tailed test?
iii) Which test of variance would you use to test whether the variability has been reduced?
Q2. Chroma, a brick & mortar electronic store, recently conducted a study on its customers. It analysed that the probability of a customer entering the store during its discount sale and buying a refrigerator or a TV set is 0.32. If the probability of a customer to buy a refrigerator is 0.21 and that of buying a TV set is 0.16, what is the probability that the customer will buy both, refrigerator & the TV set? Also comment if the events of buying the refrigerator and the TV set independent.
