Econometrics and Business Statistics (ECON634) Semester 2, 2018 Take-home Test

13
Econometrics and Business Statistics (ECON634)
Semester 2, 2018
Take-home Test

13
ANS: The distribution of numeracy scores was assumed to be normally distributed
using central limit theorem, as the sample size was greater or equal to 30.
Here, and
The required probability was calculated as below.
Figure 1: Probability Area for

13
ANS: The distribution of numeracy score was assumed to be normally distributed
using central limit theorem, as the sample size was greater than 30.
According to the problem, population parameter ratio for numeracy score was
Now, sample size
Required probability was
Figure 2: Probability Area for
ANS: Null hypothesis: H0:

13
Alternate Hypothesis: HA: where was the average numeracy score
achieved by Year 5 classes.
Level of significance was considered at 5%, and the test was a two tail test.
Sample statistic values were
Due to absence of population standard deviation, t-test was the appropriate
choice.
The t-statistic = with 58 degrees of freedom.
The p-value was < 0.05, at 5% level.
The 95% confidence interval for population mean was estimated as
, and the population average was
outside the interval.
Hence, the null hypothesis was rejected at 5% level of significance, concluding
that average numeracy scores in the three major capital cities were
significantly different from the average numeracy score of 493.
ANS: The 95% confidence interval for average numeracy score of all grade 5
classes in the major capital cities in 2015 was estimated as
, and the population average was
found to be outside the interval. Hence, the null hypothesis was correctly
rejected at 5% level of significance.
ANS: Null hypothesis: H0:
Alternate Hypothesis: HA: