1. The total shopping bills of 100 shoppers at a neighbourhood supermarket have a mean of $50 and a standard deviation of $12.50. What is the estimate of the population mean? What is a reasonable error band for this estimate? 2. A research firm conducted a survey to determine thelaverage number of cigarettes smoked per day by residents of a particular neighbourhood. A sample of 49 residents revealed that the average for the sample was 20 and with a standard deviation of 5. a. What is the point estimate of the population mean? b. Construct a 95% confidence interval for the mean. c. What if 64 smokers were sampled with the same sample characteristics? 3. A petrol station looked at the filling habits of a sample of 81 drivers and found that on the average the amount of petrol purchased is 35 litres with a standard deviation of 6 litres. Construct 90%, 95%, and 99% confidence intervals for the estimates of the population mean. 4. A random sample of 9 automobile tyres was drawn from a large production run of a certain brand of tyres. The mean life time of the tyres in the sample is 22010 miles. The sample standard deviation is 2520 miles. What is the interval estimate of the population mean at a 95% level of confidence? 5. In an election poll, it was reported that a survey of 1600 voters resulted in 60% supporting Party A and 40% supporting Party B. What is the point estimate of the proportion of the population who support Party A? Construct a 90% and a 95% confidence interval.