Economics Q Question 1 (22 marks) The data set Library2012New.sav, available on the course StudyDesk, contains infor- mation on several variables of some selected libraries including city, accreditation, year of establishment, total revenue, operational revenue, number of books and registered borrowers. Here we are interested in the accreditation status and handicapped access facility. (a) Produce a two-way (contingency) table to investigate any association betw

een ac- creditation status and handicapped access facility. [4 marks]

STA2300—Data Analysis 5 (b) Find the joint distribution of accreditation status and handicapped access facility. [4 marks] (c) In no more than 60 words, describe any special features (variation in the cell, and/or,

row/column percentages) of the joint distribution. [3 marks] (d) Find the (conditional) distribution of handicapped access facility for non-accredited libraries. [4 marks]

(e) What percentages of accredited libraries have a handicapped access facility? [3 Marks]

(f) Is there any indication of an association (relationship) between accreditation status

and handicapped access facility? Support your answer by any evidence from the data. [4 marks] Question 2 (20 marks)

The data set Library2012New.sav, available on the course StudyDesk, contains infor-

mation on several variables of some selected libraries including city, accreditation, year of establishment, total revenue, operational revenue, number of books and registered

borrowers. Here we are interested to investigate the association between the number of registered borrowers and number of children's materials in circulation. (a) Use an appropriate graph to display the relationship between the number of regis- tered borrowers and number of children's materials in circulation. [6 marks] (b) Describe the form, direction and strength of the relationship between the number

of registered borrowers and number of children's materials in circulation in about

40 words. [4 marks] (c) Calculate the value of an appropriate statistic to describe the strength of the linear association between the number of registered borrowers and number of children's

materials in circulation. [2 marks] (d) Write the equation of the regression line to predict the value of the number of

children's materials in circulation based on the number of registered borrowers. [4 marks]

(e) Use the above regression equation to predict the number of children's materials in circulation for the library having 56425 registered borrowers. [Refer to case 85 of

the data set.] [2 marks] (f) From the above predicted number of children's materials in circulation, find the residual if the observed number in circulation is 182571. [2 marks]

STA2300—Data Analysis 6 Question 3 (16 marks) The data set Library2012New.sav, available on the course StudyDesk, contains infor-

mation on several variables of some selected libraries including city, accreditation, year of establishment, total revenue, operational revenue, number of books and registered

borrowers. Here we are interested to investigate the distribution of hours open per week.

(a) Use an appropriate graph to display the distribution of the hours open per week. [4 marks] (b) Describe the shape, centre and spread of the distribution in about 50 words. [4 marks]

(c) On the same graph, display the two distributions of the hours open per week for the accredited and non-accredited libraries. [4 marks] (d) Compare the two distributions of the hours open per week for the accredited and

non-accredited libraries in no more than 60 words. [4 marks] Question 4 (16 marks) A recent business survey in Toowoomba reveals that 20% of the retail shops plan to hire new staff within the Financial year. An Economics professor at USQ takes a random

sample of 15 retail shops in Toowoomba to study the issue more thoroughly. A particular variable of interest is the number of retail shops planning to hire new staff. Based on the above information answer the following questions: (a) What is an appropriate model to represent the variable of interest? Write down the parameters of the model, if any. [3 marks]

(b) Discuss how the conditions of the above model are satisfied in the current study. [4 marks] (c) Find the mean and standard deviation of the model using the parameters of the

model. [3 marks] (d) What is the probability that at least 2 of the retail shops in the sample plan to hire new staff? [3 marks]

(e) What is the probability that no more than 2 of the retail shops in the sample plan

STA2300—Data Analysis 7 Question 5 (14 marks) How does a new vaccine protect from the Swine Flu? A pharmaceutical company prepared three levels of doses for a new Flu vaccine to be tested clinically. The first level A contained 5ml, the second level B contained 7.5ml, and the third level C contained

10ml of the actual drug. The vaccine was administered to a group of 150 randomly selected healthy adults equally divided for the three levels of doses. Another 50 randomly

selected healthy adults received a placebo. Like the health workers who administered

the vaccine, the subjects were not aware of the level of dose or placebo they received.

The incidence of Swine Flu was monitored for a period of six months, and the data were recorded for each group of subjects. (a) For the above study identify, if appropriate, (i) the response variable(s). [2 marks] (ii) the factor and its levels. [2 marks]

(iii) the experimental units. [1 mark] (b) Is this an experimental or observational study? Justify your answer in the context

of the question. [2 marks] (c) Is this a double blinded study? Explain it in the context of this study. [2 marks]

(d) What was the sample size for the study? [1 mark] (e) Are the four principles of experimental design used in this study? Explain, in the context of the study. [4 marks] Question 6 (12 marks) The height of the members of a city basketball club is distributed according to a normal

model with mean _ = 170cm and standard deviation _ = 6cm. (a) What is the probability that a randomly selected member of the club is taller than 160cm? [2 marks] (b) What proportion of the members are of height between 164cm and 182cm? [3 marks]

(c) Suppose that the tallest 10% of the members are selected for a friendly weekend match. What is the minimum height to be selected for the match? [3 marks] STA2300—Data Analysis 8

(d) What is the cutoff height for the shortest 28.1% of the members of the club? [4 marks]