#### What is the probability that the sample proportion concerned is less than 0.5?Name: EC2303 Foundations for Econometrics Matriculation #: PS3 Tutorial Section (W#): Week 6: Problem Set 3 DUE: Monday 30 September, 12pm

Hi there are 4 short statistics questions and it would be great if i could get them in 2 days. Thanks!

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Name: EC2303 Foundations for Econometrics Matriculation #: PS3 Tutorial Section (W#): Week 6: Problem Set 3 DUE: Monday 30 September, 12pm • Please hand in to the economics office (AS2 -L6) • Late assignments will not be accepted. • Show your work to get full credit. • Carry through fractions or exact decimals when possible, or round to four decimal places. Please round final answers to four decimal places. 1. (3 pts) In a given population of two-earner male/female couples, male earnings have a mean of $30,000 per year and a standard deviation of $1,000. Female earnings have a mean of $35,000 per year and a standard deviation of $1,800. The correlation between male and female earnings for a couple is 0.80. Let C denote the combined earnings for a randomly selected couple. (a) What is the mean of C? (b) What is the covariance between male and female earnings? (c) What is the standard deviation of C? 2. (3 pts) In survey taken two years ago by all employees of StatsWorld, Inc., 53% of employees were concerned about future health care benefits. This year, the company asked a random sample of only 80 employees if they were concerned about future health care benefits. Answer the following, assuming that for the entire company, the share of employees concerned about health care benefits has not changed since the first survey. (a) What is the standard error of the sample proportion who are concerned about future health care benefits? (b) What is the probability that the sample proportion concerned is less than 0.5? (c) What is the upper limit of the sample proportion concerned, such that the sample proportion concerned would exceed this value only 3% of the time? 1 EC2303 -Foundations for Econometrics Version: September 17, 2013 3. (2 pts) A town has 500 real estate agents. The mean value of the properties sold in a year by these agents is $800,000, and the standard deviation is $300,000. A random sample of 100 agents is selected, and the value of the properties they sold…

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