Question 1: [4 marks]
In an Automotive Research Association of India (ARAI) sponsored study, a random survey was done on 215 people owning petrol-driven small cars in Bangalore who had purchased their cars within the last one year. Details about the observed mileage were collected from the owners. Using the survey results, the mean was found to be 11.25 km/litre and the standard deviation was found to be 2.63 km/litre. The total number of petrol-driven small cars that were sold in Bangalore in the last one year is expected to be roughly 5500. Construct a 95% confidence interval for the average mileage of the above mentioned car population in Bangalore. Question 2: [4 marks]
The tollway management company managing the elevated flyover on Hosur Road in Bangalore is interested in knowing the proportion of Electronics City employees who actually take the elevated flyover. The company would like to be 98% certain in estimating this proportion, while it would like this proportion estimate to be within plus or minus 0.03. What is the minimum sample size that the company should use for surveying the driving route preferences of Electronics City employees in order to achieve the above desired level of precision in the proportion estimate? Question 3: [4 marks]
Two research laboratories have independently produced drugs that provide relief to arthritis sufferers. The first drug was tested on a group of 90 arthritis sufferers and produced an average of 8.5 hours of relief, and a sample standard deviation of 1.8 hours. The second drug was tested on 80 arthritis sufferers, producing an average of 7.9 hours of relief, and a sample standard deviation of 2.1 hours. At the 0.05 level of significance, does the second drug provide a significantly shorter period of relief? Question 4: [3 marks]
For Question 3 above, what is the Prob Value?