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ECON634 Econometrics And Business Statistics

tag 0 Download 6 Pages / 1,453 Words tag 18-11-2020
  • Course Code: ECON634
  • University: Macquarie University
    icon is not sponsored or endorsed by this college or university

  • Country: Australia


Question 1

A clinic offers a weight reduction program. A review of its records found the following weight losses, in pounds, for a random sample of ten of its patients at the conclusion of the program.

18.2 25.9


11.8 15.4

20.3 16.8 19.5 12.3 17.2

Assume the population distribution is normal. Use Excel to compute necessary statistics and probabilities.

(a) Find a 99% confidence interval for the population mean weight-loss.

(b) Using the result in (a), test at the 1% significance level the null hypothesis that the population mean equals 20 against the two-sided alternative.

(c) Test the null hypothesis that the population mean weight-loss equals 20 pounds against the one-sided alternative hypothesis that the population mean weight-loss is lower than 20 pounds at the 5% level.

(d) Find the p-value of the above test in (c).

(e) Suppose that the population mean is in fact 20. What is theprobability that the null hypothesis will be rejected (Type I error) in (a)?

(f) Suppose the population mean is in fact 19 and the population standard deviation is 5. What is the probability that the test

H0: ???? = 20,

H1: ???? < 20

will not reject the null against the alternative at the 5% level (Type II error)?

Question 2

Samples of size 12 were drawn independently from two normal populations. A matched pairs experiment was then conducted from the same populations. These data are stored in Excel file named “Two_samples.xls”.

  1. a)Using Excel, calculate the descriptive statistics of the two independent samples.Y X .
  1. b) Using the data taken from independent samples, test by hand to determine whether the variances of the two populations differ at the 5% significance level. Use Excel to confirm your test results and attach your Excel output table.
  1. c) Using the data taken from independent samples, test by hand to determine whether the means of the two populations differ (assume equal variance) at the 5% significance level. Use Excel to confirm your test results and attach your Excel output table.
  1. d)Repeat part (c), using the matched pairs data.
  2. e) Is the required condition for the test in part (c) and (d) satisfied? Why?
  3. f) Describe the differences between part (c) and (d). Discuss why these

differences occurred.

Question 3

Stock prices and interest rates are key economic indicators. Investors in stock markets,individual or institutional, watch very carefully the movements in the interest rate.As a measure of stock prices, let us use the S&P 500 composite index, and as a measure of the interest rate, let us use the three-month Treasury bill rate. The data on these variables are provided in Stock.xlsx for the period 1980-2007.

a) What relationship, if any, do you expect between interest rates and stock prices? Why?

b) Plot using Eviews or Excel the scattergram between interest rates (x axis) and stock prices (y-axis). Does the scattergram support your expectation in

part (a)?

c) Let ???????? be the S&P500 index and ???????? be the three-month Treasury bill rate.Using Eviews or Excel, estimate the following regression

Provide the Eviews or Excel output and write down the fitted equation (include the predictive equation, t-statistics of the estimated model parameters, and sample size).0 1

d) Interpret the coefficients. Does the sign of the slope coefficientconsistent with your expectation?
e) Test by hand the significance of the slope coefficient at the 5% significant level.

Question 4

Suppose the regression model is

The OLS estimator of the slope coefficient is

Show that the OLS slope estimator is a linear fu

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