1. The quality control manager at a light-bulb factory needs to estimate the mean life of a new type of light-bulb. The population standard deviation is assumed to be 50 hours. A random sample of 40 light-bulbs shows a sample mean life of 415 hours. Construct and explain a 90% confidence interval estimate of the population mean life of the new light-bulb.

2. In a random sample of 320 men, 18, or older, 182 were married. Construct and explain a 98% confidence interval estimate of the true population proportion of married men, 18 or older.

3. A survey of first-time home buyers found that the sample mean annual income was $51,000. Assume that the survey used a sample of 28 first-time home buyers and that the sample standard deviation was $1,200. Compute and explain a 95% confidence interval estimate of the population mean.

4. For problem #1 above, what size sample would be needed to achieve a margin of error of 12 hours or less?