Could you please help me to work out Confidence Interval questions. Thanks
1. GSK Pharmaceuticals wish to ensure that their Paracetamol tablets contain, on average, the amount quoted on the packet of their product - namely 500 mg. Clinical tests on a random sample of 69 tablets yielded an average of 500.78 mg of Paracetamol per tablet. It can be assumed, on the basis of previous trials, that the standard deviation of Paracetamol in each tablet is 6.1 mg. Construct a 97% confidence interval for the average amount of Paracetamol. Report only the upper limit (in mg) correct to two decimal places.
2. Determine the z value used to build a 90% confidence interval estimate of the population proportion. Give the positive value answer exactly as found from tables (three decimal places).
3. A market research company conducted a telephone survey of 765 Melbourne households to determine the proportion of households seeking to purchase a new car in the next two years. An interval estimate of 0.068 to 0.112 was found. Determine the level of confidence for this interval (answer as percentage to 2 decimal places).
4. Sleep apnoea is a sleep disorder that causes a person to stop breathing momentarily and then awaken briefly. A study of 524 Victorian commercial truck drivers found that 73 of them suffered from sleep apnoea. Use the survey results to estimate, with 93% confidence, the proportion of Victorian commercial truck drivers who suffer from this sleeping disorder. Report the upper bound of the interval only, giving your answer as a percentage to two decimal places.