Reference no: EM132795490

HA1011 Applied Quantitative Methods - Holmes Institute

Learning Outcome 1: Summarise numerical data and present it both by means of tables and charts
Learning Outcome 2: Be able to calculate and interpret descriptive summary measures
Learning Outcome 3: Develop simple regression models and interpret the regression coefficients
Learning Outcome 4: Understand basic probability concepts
Learning Outcome 5: Understand when to apply different distributions, their properties and how to calculate associated probabilities
Learning Outcome 6: Develop confidence interval estimates for the mean and the proportion
Learning Outcome 7: Perform Hypothesis Tests and interpret the results

Question 1

Use the following data provided in the table below to calculate the correlation "r" between the price of a product ($) and the quantity of the product purchased per week.

Price ($)	Quantity of the Product Purchased per week
10	20
20	15
30	10
30	11
40	9
80	8
90	6
90	4
120	2
130	1

a) Estimate the slope (b1) and intercept coefficients (b0) and write the equation of the regression line

Step 1: Calculate b1

Step 2: Calculate b0

Step 3: Write the equation of the regression line

b) Calculate the coefficient of determination R2 and interpret

Question 2

A survey of 800 Sydney residents resulted in the following crosstabulation regarding their major form of transport to work and whether or not they find public transport convenient.

Public Transport Convenient (Y/N)	Ferry	Bus	Train	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

a) What percentage of the Sydney residents have "Bus" as a major form of transport?

b) What is the probability of selecting a Sydney resident who does NOT find public transport convenient?

c) Among the Sydney residents who find public transport convenient, what percentage of residents indicated "Train"?

d) Assuming that a Sydney resident finds public transport convenient, what is the probability that the resident's major form of transport is "Ferry"?

e) A randomly selected Sydney resident turns out to be one whose major form of transport is the Bus. Compute the probability that the Sydney resident does NOT find public transport convenient.

Question 3

In a statistics class, a student tosses a biased coin which produces heads only 40% of the time six (6) times.
a) What is the probability that we get one head?
b) What is the probability that we get at most one head?
c) Find the mean and variance.

Question 4

The unit coordinator wants to establish the number of hours students spend studying course materials on a weekly basis. The hours are normally distributed with a mean of 19.5 and a standard deviation of 5.2. A random sample of 36 students is taken.
a) What is the probability that the average hours in the sample will be between 17.5 and 21.7?
b) What is the probability that the hours in the sample will be greater than 21.7
c) What is the probability that the hours in the sample will be less than 20.6

Question 5

Suppose we know the standard deviation of a certain population is 8. A sample size of 64 has a mean of 85.
a) Determine the 95% confidence interval estimate of the population mean.
b) Repeat part (a) with a sample size of 100.
c) Repeat part (a) with a confidence interval of 99%.
d) Describe what happens to the confidence interval estimate when:
- the sample size increases.
- Confidence level increases

Question 6

A sample of 25 items produced a mean of 46. Assume that the population standard deviation is 6. Test to determine if we can infer at α = 0.05 that the population mean is less than 50 using the following steps:
a) State the hypotheses.
b) State the relevant test statistic and the reason for the selection.
c) Level of significance.
d) Apply the Decision rule.
e) Calculate test statistics.
f) Provide a conclusion based on the above steps.

Attachment:- Applied Quantitative Methods.rar