In a certain country the distribution of income for the whole population follows a slightly right skewed distribution. Problem five: Lila programs the computer to take one thousand random samples of size 30 from the population.
In one of the thousand samples that Lila took from this population, the mean income was $34,500 and the standard deviation was equal to $3000.
a) Find the 95% confidence interval for income in the population and interpret the results.
b) What assumptions must you make when computing the confidence interval?
c) Would it be reasonable to make the following claim: "The probability that the income in the population (µ) be between the lower and the upper bound of the confidence interval calculated above is 95%" Explain. Test the null hypothesis that the mean income of the population in this country is equal to $35,000 (two-tailed test).
d) What is the long run probability of incorrectly rejecting the null hypothesis?
Problem six. USE SAME varaibles for BOTH PART A and B!!!
a) Using the sex discrimination data set to conduct a two-sample test of the mean to compare the relationship between gender and endorsing women for public office. ( outcome attitude toward putting women in public office) (Predictor Gender)
1) State the null hypothesis?
2) What is the underlying sampling distribution?
3) Using R conduct a t-test of the null and create the 95% confidence interval.
4) Using the relevant findings from the printout calculate the t value and the confidence interval by hand.
5) Interpret the results regarding testing the null and the confidence interval.
b)Conduct simple linear regression using attitude toward endorsing women for public office as outcome variable and gender as the predictor (the independent variable).
1) State the null hypothesis?
2) What is the underlying sampling distribution?
3) Using R, conduct a t-test of the null and create the 95% confidence interval.
4) Using the relevant findings from the printout calculate the t value and the confidence interval by hand.
5) Interpret the results regarding testing the null and the confidence interval.