A study by the Australian Bureau of Statistics looked at health and activity habits of various groups of Australians. It found that only 43.3 % of males aged 35-44 had participated in sufficient physical activity in the last week for health purposes. It also found that males of all ages spent an average of 12.9 hours in the last week sitting to watch television or videos (Australian Bureau of Statistics, Australian Health Survey: Physical Activity, 2011-12, Cat. No. 4364.0.55.004, 2013).

Assume you have two samples with 500 males aged 35-44 and 2000 males of all ages. Assume the values given above apply and S = 2.8 hours sitting time.

a. Construct a 95% confidence interval estimate for the mean time males sit per week to watch television or videos.

b. Construct a 95% confidence interval estimate for the population proportion of 35-44-year-old males who participate in sufficient activity per week for health.

If you want to take another survey in future, answer the following questions: c. What sample size is required to be 95% confident of estimating the population mean to within 2 hours assuming that the population standard deviation is equal to 3 hours? d. What sample size is needed to be 95% confident of being within 0.035 of the population proportion of 35-44 year old males who participate in sufficient activity if no previous estimate is available?