In this exercise you will practise interval estimation by constructing confidence intervals and considering sample size determination, as well as hypothesis testing. Question 1 is a confidence interval for a single mean with o known. Question 2 involves a hypothesis test for a single population mean, and Question 3 involves a hypothesis test for a single population proportion. Questions 4 and 5 relate to testing the equality of two means (think whether the samples are independent or paired), and finally Question 6 is a test of the equality of two population proportions. 1. A simple random sample of 225 workers in a large factory had weekly salaries with a sample mean of 2600 and a population standard deviation of $30. (a) Calculate a 99% confidence interval for the mean weekly salary of all workers in the factory. (b) How many more workers should be sampled if it is required that the estimate must be within 23 of the true average (again, with 99% confidence)? Hint: This means a tolerance of 23 - equivalent to a confidence interval width of 26. 2. A random sample of 17 observations from the population N(u, o?) yields the sample mean r = 6.73 and the sample variance s= = 1.23. At the 1% significance level, test the following hypotheses by obtaining critical values: (a) Ho : # = 6 vs. H1 : / >6. (b) Ho : #= 6 vs. H1 : p