1. An economist has measured the incomes of a population. The average income is unknown, however the standard deviation of the incomes is $4000. A) the economist considers a sample of 100 incomes from the population. With 90% confidence compute the maximum error between the average income of the sample and the true mean income of the population. B) with 90% confidence compute the minimum sample size of a sample so that error between the average of the sample and the mean of the population is $1000. 2. True or false: as the sample size increases, while all other parameters remain the same, the length of the confidence interval for the mean decreases. 3. A surveyor has found an old collection of data and statistics about heights of building in a city. The sample average of a collection of 64 buildings heights, from a particular neighborhood, is 80ft and the sample standard deviation of the heights of the 64 buildings is 24ft given this information a) determine the 90% confidence interval for true average of the heights from the data set. B) determine the 95% confidence interval for the true average of the heights from the data set.