Scenario
You are Jacky Tobin, a data analyst working for the City of Blue Lakes in their Research and Analysis department. You have been again asked by the Real Estate Institute of Victoria Chief Executive Officer (REIV CEO), Ms Inika Vera-Mae, to analyse the sample data from the recent survey of 120 house sales in Blue Lakes as part of the REIV's report on housing characteristics across various shires and municipalities. Her email to askes specific questions that you must answer.
Email from the REIV CEO
To: Jacky Tobin
From: Inika Vera-Mae
Subject: Analysis of recent housing survey data Dear Jacky,
Whilst I understand your previous reply was for 120 houses sold in the Blue Lakes region, for this analysis, please provide conclusions for all of the houses sold. That is, I have been led to believe that because your data was collected randomly, you can use your dataset to make inferences about all Blue Lakes house sales. With that in mind, I hope you are able to provide me with answers to the following questions.
1. Regarding the price of houses in Blue Lakes, can you estimate the average sale price of all houses sold?
2. Can you estimate the proportion of all houses that have brick cladding?
3. Some of my colleagues here at the REIV claim that the percentage of houses sold in the Blue Lakes region that have no heating could be less than 65% (of houses sold).
a. Is there any evidence to suggest that the proportion houses sold that don't have heating could be less than 65%?
b. Can you estimate the average house sale price (000) for the cladding types of both render and veneer houses? I am interested to learn if either cladding type has a higher average sale price.
4. A new estate has opened up very close to Blue Lakes and land sales have been high with all land sold so far revealing an average lot size of 1,245 meters squared. As Blue Lakes is an older area, I assume that the average lot size of houses sold would be less than this. Can you please confirm if my hypothesis is correct?
5. Over the years we have observed that an average of 10 new houses are built using brick as a cladding material in the Blue Lakes area each year. What is the likelihood that next year:
a. More than 10 houses will be built in Blue Lakes that have brick cladding?
b. The number of houses built using brick cladding will be 8 or less?
6. Finally, if this survey is conducted again at some time in the near future, it would be ideal if we were able to:
a. Estimate the average price of houses sold to within $45,000, and,
b. Estimate the percentage of houses sold that have no heating to within 4%.
c. Are you able to advise us on the sample size required that satisfies both these criteria?
Guidelines for Data Analysis
The analysis required for this assignment involves materials covered up to and including Topic 10 Week 10. The corresponding tutorials will also provide useful materials.
For all questions in the email, you can assume that:
- a 95% confidence level is appropriate for confidence intervals and
- a 5% level of significance (that is, alpha (α) = 0.05) is appropriate for hypothesis tests.
Although some questions can be completed using Excel (using the worksheets "CI template" and "HT template"), we strongly recommend that you do the analysis using a pen and paper approach too, as this will help you confirm your results and give you greater insight for the examination.
- Before doing any analysis, classify your data as numerical or categorical.
- Most questions will require you to complete either a confidence interval or a hypothesis test. Go through each of the questions asked by the REIV CEO and decide which technique is the most appropriate.
Below are some hints regarding the most appropriate technique:
- Do we have to make an estimate, and therefore need a confidence interval?
- Are we testing a theory/claim/or comparing values... and therefore need a hypothesis test?
- To answer some questions, you may need to make certain assumptions about the dataset we are using.
- For Question 5, you will need to calculate the probability using an appropriate probability distribution table (binomial, Poisson or normal). You could then use Excel to confirm your answer. You do not need the BlueLakesDATA_T1_2017.xlsx dataset to answer this question
Q1. From the following statements, which is the most appropriate when estimating the average House Sale Price (000) in Blue lakes?
a. The standard error is $48,345
b. We use the t distribution with 118 degrees of freedom
c. We use the normal distribution with t set at 1.645
d. We are dealing with a numerical variable measured on the ratio scale
Q2. When testing a suggestion that the average lot size is less than 1,245 meters squared, which of the following statements is correct?
a. H0: p = 1,245 m2; H1: p ≠ 1,245 m2
b. H0: p = 1,245 m2; H1: p ≠ 1,245 m2
c. H0: µ > 1,245 m2; H1: µ ≤ 1,245 m2
d. None of the pairs of hypotheses presented above are correct
Attachment:- BlueLakesDATA.rar