Estimation examples 2016-2017

Statistical inference is the procedure by which we reach a conclusion about a population on the basis of the information contained in a sample drawn from that population.  Estimation involves the use of the data in the sample to calculate the corresponding parameter in the population from which the sample was drawn.
A point estimate is a single numerical value used to estimate the corresponding population parameter.
An interval estimate consists of two numerical values that with a specified degree of confidence, we feel includes the parameter being estimated.Suppose a researcher , interested in obtaining an
estimate of the average level of some enzyme in a
certain human population, takes a sample of 10
individuals, determines the level of the enzyme in
each, and computes a sample mean =22
Suppose further it is known that the variable of
interest is approximately normally distributed with a
population variance of 45. We wish to estimate ?. (?=0.05)
A research team is interested in the difference between serum uric acid levels in patients with and without Down s syndrome.  
In a large hospital for the treatment of the mentally retarded, a sample of 12 individuals with Down s syndrome yielded a mean of   = 4.5 mg/100 ml.  In a general hospital a sample of 15 normal individuals of the same age and sex were found to have a mean value of = 3.4 mg/100 ml.  If it is reasonable to assume that the two populations of values are normally distributed with variances equal to 1 and 1.5, find the 95% confidence interval for