Maths and Stat問題

1) The editor of a publisher wants to estimate the mean number of errors in a book within ±1.5 error per book at 95% confidence level. What is the sample size required to do this, given that the standard deviation of 4.7 errors per book.

2) The manager of a company wants to estimate the market share of its product with 90% chance that the error of the estimate is less than 1%. How large should the sample be?

3) In a survey of 1025 randomly selected adults in Hong Kong, 298 of them mention that they use the Internet for shopping at least a few times a year. Find the 99% confidence interval estimate of the percentage of Hong Kong adults who use the Internet for shopping.

4) Air pollution is a problem in Hong Kong. The Environmental Protection Agency has established an air quality standard for lead : 1.5 micrograms per cubic meter. Listed below are measured amounts of lead ( in micrograms per cubic meter ) in the air of Hong Kong.
0.73 1.10 0.42 5.40 1.10 0.48
Use the given data to construct a 95% confidence interval estimate of the mean amount of lead in the air in Hong Kong and briefly comment on the air quality in Hong Kong.