Use the 7 Step Process of Statistical Hypothesis Testing

Question 1

One of the continuing concerns industry is the increasing cost of health insurance for its workers. In 1993 the average cost of health premiums per employee was R2,851, up 10.5% from 1992 (Nation's Business, Feb. 1995). In 1997, a random sample of 23. companies had a mean health insurance premium per employee of R3,321 and a standard deviation of R255. a) Use a 99% confidence interval to estimate the mean health insurance premium per employee for all companies. b) Test at 99% whether the true mean health insurance premium per employee in 1997 exceeds R2,851, the 1993 mean.

Question 2

A salary survey conducted on behalf of the Institute of Management Accountants and the publication Management Accounting revealed that the average salary for all members of the Institute was R6391. A random sample of 122 members from Cape Town were questioned and found to have a mean salary of R6770 and a standard deviation of s = R2892. a) Assume that the national mean is known with certainty. Do the sample data provide sufficient evidence to conclude that the true mean salary of Institute members in Cape Town is equal to the National Average? b) Suppose the true mean salary for all Cape Town members is R6391 c) Find 95% confidence interval to estimate the true mean salary of Institute members in Cape Town.

Question 4 The variability in unit mass is very critical in the pharmaceutical industry. The mass, in grams, of each of 15 randomly selected units of a specific drug is as follows. 3.48 3.52 3.50 3.47 3.49 3.54 3.51 3.52 3.46 3.45 3.55 3.48 3.51 3.52 3.50

a) Assuming that this sample comes from an underlying normal population, test the hypothesis that the mean of the population exceeds 2.2 gm^2

b) Find 95% confidence intervals