3-4. Suppose that the true mean of a variable is 20, and that the variable has a standard deviation of 6. You draw repeated samples of 40 respondents from the population and calculate the mean of the variable in each one. In what range will about 95% of your calculated means fall? Report the lower end of the range for problem 3, and the upper end of the range for problem 4 (1 point each). 5-6. You have been asked to determine the proportion of residents in your city who are immigrants. You draw a random sample of 300 residents and find that 0.35 of your sample is composed of immigrants. Calculate a 99% confidence interval for this proportion. Report the lower end of confidence interval for problem 5, and the upper end of the confidence interval for problem 6 (1 point each). 7. Interpret the 99% confidence interval you calculated in the previous problem. (2 points) 8. A survey company polls 3,560 voters about whether they plan to vote for the Liberal or the Conservative candidate. They find that 51% of voters prefer the Liberal candidate. The company asks you to advise them whether they can declare the Liberal candidate the likely winner, with no more than a 5% chance of being wrong. What is your advice? Why?' (4 points) SPSS Exercise