Assignment:
1. The average worker's hourly wage is stated to be $26.50 in a particular city. A researcher believes that the city's average salary is lower than that. The researcher surveys 45 randomly selected workers in the city and fords their average hourly wage is $24.30. The sample standard deviation is $5.42. With alpha=0.01, does the researcher have evidence to support their claim? For full credit, show your work, report your t-score and critical value(s), and explain how you arrived at your answer.
2. Use the accompanying data set to answer this question ("Problem set 2 data.xlsx"), worksheet "Problem 2". The education data come from a random sample.
a) Calculate and report the sample mean, standard deviation, and sample size. Round your answer to 3 decimal places.
b) What are the degrees of freedom if you wanted to construct a confidence interval for the population mean?
c) Using the information in a and b, construct and report the 90%, 95%, and 99% confidence intervals for the population mean (in interval format, not +/- format). Round your answers to three decimal places. What happens to the intervals as you increase the confidence level? Explain in 1-2 sentences.
3. For each of the following regression equation estimates (which are based on random samples), interpret the slope coefficient, 13-hat (i.e., ceteris paribus, what is a 1-unit or 1% increase in the independent variable associated with?), and fmd the value of the y-variable for the given value of the x-variable.
a) Wages, = 10.3 + 3.9*Experience, ("Wages," = $/hr of person i; "Experiencei" = number of years the worker has been employed). Compute Wages when Experience=10 years.
b) Unemploymentt = 7.7 - 1.1 *Growth rates ("Unemploymentt" = unemployment rate in year t; "Growth ratet" = growth rate in year t). Compute Unemployment when the growth rate is 2.5%.
c) Quantity Demandedi = 18.7 - 0.4*Pricei ("Quantity Demandedi" = amount of product i demanded; "Price," = price of product I). Compute the quantity demanded when the price is $4.50.
4. Use the accompanying dataset to answer this question ("Problem set 2 data.xlsx"), worksheet "Problem 4". The data come from the U.S. Census and California Department of Justice.
a) Estimate a linear regression model where property crime is the dependent variable ("y" variable) and population density is the independent variable ("x" variable). Report the intercept and slope coefficients.
b) Is the slope coefficient significant at alpha=0.05? Explain how you arrived at your answer.
c) San Bernardino County has a population density of 103.6. What is the predicted value of property crime, based on your results in part a?
d) Compare what you found in part c to the actual level of property crime in San Bernardino County. Does your model over or underestimate the amount of property crime in San Bernardino County? Discuss in 1-2 sentences.
Attachment:- Property Crime Rate.rar