PLEASE SHOW WORK SO I UNDERSTAND THIS:

• The average life expectancy of people around the world is 71.30 years with a population standard deviation of 8.00 years. I take a sample of 50 countries now and find that the average life expectancy is 74.37 years. Suppose Im interested in seeing if there has been a significant increase in the life expectancy.
  • a)What is the standard error?
  • b) What is the margin of error at 90% confidence?
  • c) Using my sample of 50, what would be the 90% confidence interval for the population mean?
  • d) If I wanted to control my margin of error and set it to 1 at 95% confidence, what sample size would I need to take instead of the 50?
  • e) What are the null and alternative hypotheses?
  • f) What is the critical value at 90% confidence?
  • g) Calculate the test statistic.
  • h) Find the p-value.
  • i) What conclusion would be made here at the 90% confidence level?