Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
INSTRUCTIONS TO CANDIDATES: READ CAREFULLY
1. A template answer sheet has been provided with this assessment.
2. All mathematical/statistical workings should be shown. In Part A, where necessary you may use the Microsoft Word Equation Editor (or similar) or hand-written mathematical/statistical workings and paste these within your answers. However, for Part B you must
type all of your answers, again, where necessary you may use the Microsoft Word Equation Editor (or similar).
3. Where necessary, you are expected to use the t-tables and z-
tables at the end of this examination paper to answer questions in Part A, rather than using external sources or software.
4. You should use STATA only for part B2 of this examination. You are expected to use a Casio fx-83 or Casio fx-85 calculator (or
similar) for the remainder of this examination, where the calculator does not have advanced mathematical/statistical functions.
5. Although you have up to 3 hours to submit your answers from the time the exam opens. You will be granted an additional 30 minutes to upload your answers.
6. Save your work regularly, at least every 15 minutes.
7. Answer all questions.
8. Label each answer very clearly so that markers can see easily to which question they belong. Answers should be submitted in order.
ONLINE SUBMISSION INSTRUCTIONS:
1. Your answer sheet should be submitted via the Turnitin submission link titled ‘FINAL ASSESSMENT’ on the module KEATS page.
2. Ensure your document is submitted as CANDIDATE ID – MODULECODE- i.e. A12345 4SSMN103
3. Once submitted please check you are satisfied with the uploaded document via the submission link.
4. If you experience technical difficulties uploading your assessment to KEATS please email a copy to [email protected] with the subject as CANDIDATE ID- MODULE CODE- PERIOD 2 ASSESSMENT
SECTION A (36 marks)
Answer ALL questions. Each question carries 6 marks.
QUESTION A1
a) Suppose a player plays a game of chance with probability 0.45 that they are successful and 0.55 that they fail. What is the probability that they will win four times if they play the game seven times? (3 marks)
b) ‘One of the assumptions of the binomial distribution is that the trials are independent’. Is this statement true or false? Explain (3 marks)
QUESTION A2
a) A florist is interested in the number of customers who purchase bunches of flowers in an hour. Suppose the population mean
number of purchases from florists in the locality is 15 bunches of flowers per hour, with a population variance of 4. What is the
probability that the florist will sell equal or less than 12 bunches of flowers in an hour. (3 marks)
b) Explain why we often use sample means and variances instead of population means and variances in statistical analysis. (3 marks)
QUESTION A3
Marcella investigates reviews for a particular hotel by accessing a hotel review site. She finds that 75% of all reviews were good. Of the
positive reviews, 25% were by people aged more than 40. 60% of the reviews were written by people aged less than 40.
a) What is the probability that Marcella reads a positive review and it was written by a person aged more than 40? (2 marks)
b) What is the probability that a review was positive and the review was written by a person aged less than 40. (2 marks)
c) What is the probability that the review was written by a person aged less than 40 given that it was positive? (2 marks)
QUESTION A4
The following ANOVA table represents the estimates calculated by a researcher who wants to test for equality of mean waiting times in six hospitals, based on samples of 10 patients in each hospital. The F critical values are also shown in the table.
ANOVA table for hospital waiting times:
|
degrees of freedom |
Sum of Squares |
Treatments |
5 |
220 |
Error |
54 |
630 |
Total |
59 |
850 |
|
|
|
F(5,54), 95% = 2.39, 99% = 3.38 |
a) State the null and alternate hypotheses (1 mark)
b) Using an F test, can the researcher be 95% sure that there is a difference between the test pass rates across centres? Can they be 99% sure? (3 marks)
c) What are the limitations associated with the ANOVA test? (2 marks)
QUESTION A5
A large UK firm purchases supplies from firms, of which some are domestic (D) firms, some are located in Italy (I) and some are located in China (C). In one year some suppliers deliver on time (O) and some deliver late (L). The following table shows the joint probabilities of supply country and timeliness.
Joint probability table:
|
D |
I |
C |
O |
0.45 |
0.14 |
0.11 |
L |
0.18 |
0.08 |
0.04 |
a) Calculate the marginal probabilities for each country and for O and L (1 mark)
b) What is the probability that: (2 marks)
(i) The supplier is a domestic firm given that the supplies are on-time? (1 mark)
(ii) The supplies are late given that they come from Italy? (1 mark)
c) Suppose the prices charged for the supplies by D, I and C are £1000, £1,500 and £750, respectively. Calculate the conditional expectation of the supplier price given L. (3 marks)
QUESTION A6
a) Define prior and posterior probabilities. (2 marks)
b) Suppose that an events management company estimates the probability that a customer attending an event pays on-line (A1) is 0.55 and their probability of paying at the door (A2) is 0.45. Market research suggests that 80% of payments on-line and 15% of payments at the door are by people in the 18-30 age group. Using Bayes theorem, calculate the posterior probability that those attending the event aged 18-30 will pay on-line.