Quantitative Methods
Question 1 (8 marks = 2 + 2 + 2 + 2)
A company is having a new website developed. In the final testing phase the download time to open the new home page is recorded for a large number of computers in home and office settings. The mean download time for the site is 2.5 seconds. Suppose that the download times for the site are normally distributed with a standard deviation of 0.5 seconds. If you select a random sample of 30 download times,
a. What is the probability that the sample mean is less than 2.75 seconds?
b. What is the probability that the sample mean is between 2.70 and 2.90 seconds?
c. The probability is 80% that the sample mean is between what two values symmetrically distributed around the population mean?
d. The probability is 90% that the sample mean is less than what value?
Question 2 (9 marks = 3 + 3 + 3)
At a large south-east Asian airport flights are classified as being on time if they land less than 15 minutes after the scheduled time. A study of airlines using the airport finds that a Middle Eastern airline has the lowest proportion of late flights, 0.149. Suppose you have been asked to perform a follow up study for this airline in order to update the estimated proportion of late arrivals. What sample size would you use to estimate the population proportion to within a an error of
a. ± 0.06 with 95% confidence?
b. ± 0.04 with 95% confidence?
c. ± 0.02 with 95% confidence?
Question 3 (8 marks = 2 + 2 + 2 + 2)
The owner of a petrol station wishes to study the petrol-purchasing habits of customers at her station. You select a random sample of 60 motorists during a certain week with the following results.
• Amount purchased: = 42.8 litres, S = 11.7 litres.
• 11 motorists purchased premium unleaded petrol.
a. At the 0.05 level of significance, is there evidence that the mean purchase is different from 38 litres?
b. Find the p-value in (a).
c. At the 0.05 level of significance, is there evidence that fewer than 20% of all her service station customers purchase premium unleaded petrol?
d. What is your answer to (a) if the sample mean equals 39 litres?
Question 4 (13 marks = 2 + 2 + 2 + 2 + 2 + 2 + 1)
An event organiser would like to predict the number of ‘portaloo’ lavatories required for outdoor entertainment events based on the volume of food to be consumed at the event. The organiser has collected the following data.
Number of lavatories Volume of food consumed (Kg)
17 125
121 875
93 723
17 154
66 469
48 350
119 1156
108 1000
67 500
81 683
104 723
28 256
65 523
a. Plot a scatter diagram for this data. Describe (briefly) the relationship between the volume of food consumed and number of portaloos.
b. Assuming a linear relationship, calculate the regression equation for this data. Please show your calculations or insert your summary output from Excel.
c. Interpret the estimated Y intercept, , and the estimated slope, .
d. Perform residual analyses and determine whether the sample data meet the regression assumptions of equal variance (homoscedasticity) and normality.
e. Is the amount of food consumed a statistically significant predictor of portaloos? Please explain your answer.
f. Comment on the goodness of fit of this model.
g. Predict the number of lavatories if event attendance is 50,000.
Question 5 (12 marks = 2 + 2 + 2 + 3 + 3)
The traffic controller at Sydney’s Kingsford Smith International Airport believes that the main reasons for late aircraft departures are external to the airport management—namely, late aircraft arrivals and mechanical failures. In a report to management discussing this issue the traffic controller decides to test his assertion using data collected from a random sample of 20 days.
No. of delays No. of late arrivals No. of mechanical problems
4 2 3
8 5 6
1 0 1
0 0 1
7 4 3
2 1 1
0 1 1
0 1 1
3 2 1
4 4 0
2 2 0
8 6 2
12 6 5
5 4 2
3 2 1
0 1 0
2 1 1
6 4 2
13 10 3
7 3 4
a. Write out the estimated multiple regression equation. Please show your calculations or insert your summary output from Excel.
b. Interpret the meaning of the slopes b1 and b2 in this equation.
c. Predict the number of delayed flights if four aircraft arrive late and there are three mechanical failures.
d. Comment on the goodness of fit of the estimated regression model.
e. Is there a significant relationship between the number of delays and the two independent variables (number of late arrivals and number of mechanical problems) at the 0.01 level of significance?
On the basis of these results indicate the most appropriate regression model for this data.
ORDER THIS ESSAY HERE NOW AND GET A DISCOUNT !!!
Our Service Charter
-
Excellent Quality / 100% Plagiarism-Free
We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers. -
Free Revisions
We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed. -
Confidentiality / 100% No Disclosure
We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service. -
Money Back Guarantee
If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit. -
24/7 Customer Support
We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.