HA1011 Applied Quantitative Methods Assignment

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HA1011 Applied Quantitative Methods Assignment - Holmes Institute, Australia

Assessment Task - Tutorial Questions

Purpose: This assignment is designed to assess your level of knowledge of the key topics covered in this unit.

Unit Learning Outcomes Assessed:

1. Understand the pitfalls and benefits of statistics.

2. Distinguish between the different survey sampling methods.

3. Summarise numerical data and present it both by means of tables and charts.

4. Be able to calculate and interpret descriptive summary measures.

5. Develop simple regression models and interpret the regression coefficients.

6. Understand basic probability concepts.

7. Understand when to apply different distributions, their properties and how to calculate associated probabilities.

8. Develop confidence interval estimates for the mean and the proportion.

9. Perform Hypothesis Tests and interpret the results.

Description: Your task is to answer a selection of tutorial questions for weeks 1 to 5 inclusive and submit these answers in a single document. The questions to be answered are;

Question 1 - Based on the following table, calculate the three (3) measures of central locations and briefly discuss what each statistic tells you.

23	30	25	28	36	26	38	45	52	22
33	24	29	41	39	38	48	55	44	19
18	31	34	45	75	61	72	29	27	55

Question 2 - Refer to the table below. Consider the relationship between the number of houses sold (Y) and the mortgage rate (X). The values of X and Y for twelve (12) months are shown in the table below.

M-Rates	8	9.5	7.5	11	8.5	10	10.5	7	7.5	11	9	8
House sold	188	145	181	137	157	148	140	203	188	144	150	166

Based on that,

a. Calculate the coefficient of correlation between the number of houses sold and the mortgage rate.

b. What does the correlation coefficient tell you about the relationship between the level of house sales and mortgage rates based on the calculation?

Question 3 - In seeking to determine how influential advertising is, the management of a recently established retail chain collected data on sales revenue and advertising expenditure from its' stores over the last ten (10) weeks. The table below shows the data collected:

Advertising Expenditure ($000)

3.5

4.5

7.5

8.5

Sales ($000)

250

700

450

150

200

750

800

1,100

a. If they are going to run a linear regression, identify which variable should be the independent variable and which should be the dependent variable in a regression equation.

b. Estimate the slope and intercept coefficients of the linear regression model.

c. If advertising expenditure is equal to $9,000, estimate the total sales income.

Question 4 - A retail shop manager analyzed the relationship between sales and the method of payments. Based on his analysis, he has produced the following joint probability table, as shown below:

Size of purchase	Method of payment
Size of purchase	Cash	Credit Card	Debit Card
Under $20	0.09	0.03	0.04
$20 - $100	0.05	0.21	0.18
Over $100	0.03	0.23	0.14

a. What proportion of purchases were paid by debit card?

b. What proportion of purchases were paid by cash?

c. Determine the proportion of purchases made by credit card or by debit card?

d. Are the events "payment by cash" and "purchase of under $20" mutually exclusive? Explain your answer.

Question 5 - a. Given the following probabilities, calculate all the joint probabilities.

P(A) = 0.9

P(A^-) = 0.1

P(B/A) = 0.4

P (B/A^-) = 0.7

b. A coin is flipped three (3) times. Use a probability tree to find the probability of observing:

i. No heads

ii. Exactly one head

iii. Exactly two heads

iv. At least one tail

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