interval estimation

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 30 light-bulbs shows a sample mean life of 475 hours. Construct and explain a 90% confidence interval estimate of the population mean life of the new light-bulb.

2. A survey of first-time home buyers found  that the sample mean annual income was $46,000. Assume that the survey used a sample of 20 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.

3. A telephone poll of 750 American adults asked "where would you rather go in your spare time?"  One response, by 275 adults, was "the Mall". Compute and explain a 99% confidence interval estimate of the proportion of all American adults who would respond "the Mall".

4. For problem #1 above, what size sample would be needed to achieve a margin of error of 15 hours or less?