Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

First Mid-term exam.

Economics 312

Summer 2022

Answer Question 3.  Choose one from Questions 1 and 2.

1. In the following picture, two standard normal (Z) curves are presented under two scenarios – the left curve representing the scenario when H₀ is true and the right one representing the scenario when H_a is true.  The red vertical line represents critical value (Z_α) for a right-tailed test.  Answer the following questions using the alphabets representing specific regions in the hypothesis test situation:

Answer QS # 1 Here:

(i) Type I Error =

(ii) Type II Error =

(iii) Power of the test =

(iv) 1 - α =

2. Suppose the two random variables and  are related in the following way:

(i) Find ( variance of ) in terms of .

(ii) Find (covariance between  and ) in terms of .

(iii) Find the correlation () between  and .

Answer QS # 2 Here:

3. The following EXCEL file containing the demand for gasoline data has been uploaded on the iLearn site: DEMGAS.  Do the following in sequence:

(i) Use EXCEL’s “Data Analysis” feature “Descriptive Statistics” to produce summary statistics of the following variables: Q, P, Y.  Make sure you include the name labels of Q, P, Y while producing the summary statistics and report the output on the same EXCEL sheet and not in a different worksheet.

Copy and Paste Summary Statistics Here (Copy and paste the summary statistics from EXCEL here):

(ii) Write down the formulas and the corresponding numerical values of the following quantities:

Answer QS # 3 (ii) Here:

· Standard Error:

· Standard Error:

· Standard Error:

(iii) Assume that this sample of 37 years is a random sample and the sample observations for each Q, P, and Y are drawn from a normal distribution.  Test if the population mean per-capita annual consumption of gasoline has exceeded 200 gallons during the relevant years.  Show all the steps for hypothesis test for this problem BELOW.  Test this hypothesis at 1% level of significance.

Answer QS # 3 (iii) Here:

(iv) Find the p-value for this test.  Explain what this p-value means and how you use this information to reject or accept the null hypothesis.

Answer QS # 3 (iv) Here:

(v) Use the EXCEL’s “Data Analysis” feature “Correlation” to produce the correlation matrix for this sample for the following variables: Q, P, and Y.  Make sure you include the name labels of Q, P, Y while producing the correlation matrix and report the output on the same EXCEL sheet and not in a different worksheet.

Answer QS # 3 (v) Here (copy from EXCEL and paste the correlation matrix here):

(vi) Write down the values of the following two pairwise correlations: (a) Q versus P and (b) Q versus Y.  Interpret in one sentence each the two sample correlation coefficients.  

Answer QS # 3 (vi) Here: