Econ 2310: Business Statistics

Problem Set #3

 

Instructions: You may work with up to 3 other of your classmates on this project. Please show all work. Due online by Sunday, April 30^th, 2017.

 

1.)     Proportions (30 points)

On April 15^th, 1912, the R.M.S. Titanic sank into the North Atlantic Ocean, resulting in the loss of more than 1,500 passengers and crew. Below is a table which summarizes the total number of passengers and the number of survivors for the crew, first-, second-, and third-class.  Find the proportion of survivors by type of service (crew, first, second, third). Test the hypothesis at the 95% confidence level that the proportion of first-class survivors is the same as the proportion of third-class survivors. What do you calculate for the test-statistic? What is the critical statistic? What is the conclusion of your hypothesis test?

 

 

2.)    Hypothesis Testing

What is a type I error? What is a type II error? For a test at the 95% confidence level, what is alpha? What is the power of a statistical test?

3.)     Sample Size

You work in the leasing office of GE capital and wish to predict the average mileage driven of your leased cars within a margin of error of 100 miles (you need this for your company’s financial disclosures). Suppose your average customer drives 10,000 miles a year, and your guess for the standard deviation is about 500 miles. How big of a sample size do you need to generate a 95% confidence interval with a mean of 10,000 miles a year with a margin of error of 100 miles?

 

 

 

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