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Business Maths/Quantitative Analysis

Question 1
A machine fills boxes of fish fingers to a mean volume of 368 grams with a standard
deviation of 15 grams. Assume that the volumes in the bottles are normally distributed. If a
sample of 25 boxes is randomly selected:

a. What is the probability that the sample mean will be below 368g? (3 Marks)
b. What is the probability that the sample mean will be below 360 grams? (3 Marks)
c. What is the probability that the sample mean will be between 360 grams and 370
grams? (3 Marks)
d. Now assume that we did not know the population mean amount in the boxes and all
we know is that the amount of fish finders in individual boxes are normally
distributed. Now you select a random sample of 25 boxes and find that the sample
mean is 365 grams and the sample standard deviation is 10 grams. Set up a 95%
confidence interval for population mean. (4 Marks)
Question 2
Theory suggests that level of education and experience are two major components of a
wage equation. In this question, we are trying to estimate an equation for hourly wages for
a sample of 901 households. Data as described below are stored in excel file
Assignment2_Q2.xls.

Wage = earnings per hour
Educ = years of education
Exper = experience in years

Consider a regression of the form:

01 iii
WageEduc ββε =++ —- (Model 1)

e. Construct a scatter plot of wage and education. Does there appear to be a relationship
between the variables? (2 Marks)
f. Estimate the above regression model using excel. Write down the estimated
regression line. (3 Marks)
g. Interpret the coefficient on education. (3 Marks)
h. According to your regression, what is the expected wages for an individual who has
completed a 12 years of education? (3 Marks)
i. Comment on the goodness of fit of the model. (3 Marks)
ow consider the multiple linear regression model below.
011 iiii
WageEducExper βββε =+++ —— (Model 2)
j. Construct a scatter plot of wage and experience. Does there appear to be a relationship
between the variables? (2 Marks)
k. Now estimate Model 2 and write down the estimated regression line. (3 Marks)
l. Interpret the coefficient on education and experience. (3 Marks)
m. Does inclusion of experience improve the model? Consider the goodness of fit of
your models when answering this question. (3 Marks)
n. Assuming that all the assumptions are satisfied, at 5% significant level find whether
the level education increases hourly wage rate. (6 Marks)
o. Assuming that all the assumptions are satisfied, at 5% significant level find whether
we have sufficient evidence to suggest that experience is a significant variable in the
model. (6 Marks)

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