Econometrics UE Past Papers Questions.


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(2933) Question Category: Mathematical Calculation

The Chi-square contigency test statistics is widely used in economic analysis

  1. What is the purpose of using such a test -statistics?
  2. Give an example of a typical situation where this test statistic will be appropriate
  3. A formula for calculating a chi-square contigency test statistics is given as

X^{2}=sum_{i=1}^{r} sum_{j=1}^{c}frac{(o_{ij}-e_{ij})^{2}}{e_{ij}}  with d.f=(r-1)(c-1)

o_{ij}= observed frequency in cell(i,j)

e_{ij}= expected frequency in cell(i,j)

r= number of rows

c=number of columns

Using the data presented below calculate a chi-square contigency test statistic for variable X and Y

Variable (X) Variable (Y)
Y11 Y12
X11 12 108
X12 24 156
  1. Test the hypothesis that X is independent of Y at alpha (alpha)=5%. Note that x^{2}.05=3.841
  2. What is your conclusion at this level of significance?

Answer / Solution

UNSOLVED

(2934) Question Category: Mathematical Calculation

A confidence interval is calculated as ar{x}pm Z_{frac{alpha}{2}}frac{sigma }{sqrt{n}}. A researcher from Mzumbe University observed that in a sample of 28, the mean was 1.68 and sample variance was 0.71

  1. Construct a 95% confidence interval for mu. Assume that the sample was drawn from a normal distribution. Note that t_{frac{alpha}{2}}=2.064
  2. What is the meaning of this confidence interval?
  3. Another researcher claims that the population mean is 2.5. At this level of significance.
  1. State the null and alternative hypothesis
  2. Test the null hypothesis.

Answer / Solution

UNSOLVED

(2935) Question Category: Mathematical Calculation

The OLS fitted line explaining college GPA in terms of high school GPA and ACT score is estimated as:

ColGPA=1.29+0.453GPA+0.0094ACT

  1. Interpret the intercept and slope coefficient
  2. Using the information provided above , complete the following table
Observed value of college GPA 3.4 3.5 3.6 2.8 3.1 2.9 2.8 2.5
Predicted value of college GPA                
GPA 3 3.2 2.8 2.6 2.9 3.5 3.8 3.9
ACT 24.2 25.6 25.8 26 26.2 26.4 26.6 26.8
Predicted error                

 

Answer / Solution

UNSOLVED

(2936) Question Category: Mathematical Calculation

Use the information provided in the table below to answer questions that follows

Observed data for variables X and Y

Observation No Observed values of X Observed values of Y
1 2 4
2 4 6
3 5 8
4 7 9
5 8 12
6 11 16
7 13 21
8 15 17
9 16 20
10 19 25
  1. Calculate the estimators of alpha (alpha) and Beta(eta) in the folowing regression model

y=alpha +eta x + varepsilon

hat{alpha}=ar{y}-hat{eta}ar{x}

The estimators can be calculated as hat{eta}=frac{sum(x_{i}-ar{x})(y_{i}-ar{y})}{sum(x_{i}-ar{x})^{2}}

  1. State the null and alternative hypothesis that arre needed to test whether the slope coefficient is zero.

Answer / Solution

UNSOLVED

(2937) Question Category: Short answers

What is the meaning of the following terminologies / concepts as used in econometrics

  1. Asymptotic unbiasness
  2. Asymptotic efficiency
  3. Serial correlation
  4. Logistic regression
  5. Heteroskedasticit

Answer / Solution

UNSOLVED

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