Economics 1010a1 Lecture 1: COMPLETE Summary Statistics (Quantitative Methods II (EconomicsBEFE))

The USA Today reports that the average expenditure on Valentine's Day is $100.89.Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 30 female consumers was $68.64, and the average expenditure in a sample survey of 40 male consumers was 135.67. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20.

a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?

b.At 99% confidence, what is the Margin of Error?

c.Develop a 99%confidence interval for the difference between two population means.   

Answer the following questions in one or two well-constructed sentences.

a. What happens to the standard error of the mean if the sample size is increased?

b. What happens to the distribution of the sample means if the sample size is increased?

c. When using the distribution of sample means to estimate the population mean, what is the benefit of using larger sample sizes?

Assume that we draw two random samples of students from Coles College of Business. One group includes 10 economics majors and another includes 30 finance majors. From these two groups, we obtain the following statistics regarding the performance on the final calculus exam: Economics: the average value is 87, the standard deviation is 9; Finance: the average value is 91, the standard deviation is 5. Please conduct a 90% significance test for the equality of the two population variances and state if such a test would reject or not the null hypothesis that the two variances are equal.