Sample STT500 Statistics for Decision Making Assignment 2

STT500 Statistics for decision making Assignment 2 Sample

Description

The individual assignment must provide a 1500-word written report. This report for The Assignment Helpline will develop students' quantitative writing skills and test their ability to apply theoretical concepts covered from weeks 1-8. Please use Excel for statistical analysis in this assignment. Relevant Excel statistical output must be properly analysed and interpreted.

Assignment Data

The real estate markets present a fascinating opportunity for data analysts to analyse and predict property prices. Considering the data provided a large set of property sales records.

Attribute information:

PN: Property identification number • Price: Price of the property ($000) • Bedrooms: Number of bedrooms

• Bathrooms: Number of bathrooms

Lot size: Land size (in square meters)

The population property data from which you will select your sample data consists of 500 IDs each with an identifying property number (PN) ranging from 1 (or 001) to 500.

Your first task is to select 50 three-digit random (property) numbers ranging from 001 to 500 from the provided table of random numbers.

To select your 50 random property identification numbers, you will need to first go to a starting position row and column in the random number table. Defined by the last three digits of your Polytechnic Institute Australia student identification number. The last two digits of your PIA ID number identify the row, and the third last digit identifies the column of your (relatively) "unique" starting position.

You need to record these first three acceptable ID numbers into the first column of an Excel spreadsheet and then continue this process until fifty valid three-digit personal identification numbers are selected.

To select your sample data based on 50 randomly selected properties from the random number table, you will need to use these identification numbers to select properties from the Excel sheet of the population property data.

For the demonstration last three digits of 205, reading across row 05 from left to right starting at column 2 as instructed, you would encounter the following three-digit numbers.

04773 12032 51414 82384 38370 00249 80709 72605 67497

You need to record these first three acceptable ID numbers, 047, 120, 383 and 002 into the first column of an Excel spread-sheet and then continue this process until fifty valid three-digit personal identification numbers selected.

Students are required to use the generated data according to their student ID to answer the assessment questions.

Make sure the following questions are covered in the data analysis:

1) Create 50 randomly selected properties from the random number table based on your PIA ID number, you will need to use these identification numbers to select properties from the Excel sheet of the population property data. Use your data to answer questions 2-10.

2) Use Excel to create frequency distributions, Bar charts, and Pie charts for the number of bedrooms and bathrooms. Comment on the key findings.

3) What type of variable (Continuous, Discrete, Ordinal, or Nominal) is the number of bedrooms, and justify your answer.

4) Use Excel to create Histogram for the Price of the property and Land size (square ft lot). Also. Comment on the key findings.

5) Show descriptive summary statistics for the Price of the property in thousand dollars and Land size (square ft lot). Comment on the shape, canter, and spread of these two distributions.

6) Check the normality of the Price of the property data with three pieces of evidence.

7) Construct a 95% confidence interval for the population's average Price of the property, also Interpret the confidence interval.

8) Construct a 95% confidence interval for the population's average Land size (square ft lot) of the property, also Interpret the confidence interval.

9) Test whether the population's average Price of the property in thousand dollars is different from $530. Formulate the null and alternative hypotheses. State your statistical decision using the significant value (a) of 5%.

10) State your conclusion in context.

Solution

Task 1: Selecting Random Sample

1. Based on ID 20241288, last 3 digits are: 288, In my ID 88 identifies row and 2 identifies the
column in the random number table.

Data Table

Task 2: Use Excel to create frequency distributions

2. Frequency Distribution, Bar charts and Pie chart for number of Bedrooms and bathrooms

Task 2: Use Excel to Create Frequency Distributions

2. Frequency Distribution, Bar charts and Pie chart for number of Bedrooms and bathrooms

Table 1: Frequency Distribution
(Source: Ms Excel)

The key finding from the frequency distribution of bathrooms, therefore, is that number of bathrooms is an ordinal discrete variable, by which we mean that it is a ranked variable with defined, separate values (i. e. 1, 1. 5, 2 and so on). The bar chart shows the frequency and distribution of the number of bathrooms which is protracted to show the most frequently occurring bathroom count among the buildings. This aspect of the visualization is informative about how the bathroom availability is usually distributed in the properties and a way of giving an estimate of which bathroom count is more popular among the properties in the data set in helping to decipher the general pattern of these homes.

Figure 1: Bar chart of bedroom frequency Distribution
(Source: MS- EXCEL)

Interpretation: This bar chart relates to the distribution of the number of bedrooms in the properties. This bar advertises how many of them have a certain number of bedrooms. For instance if out of 100 properties the majority of them have 3 rooms, then the bar corresponding to 3 rooms shall be the highest. In particular, this visualization makes it easier to determine which frequency of bedrooms is typical of the sampled properties.

Figure 2: Barchart of Bathroom frequency Distribution
(Source: MS- EXCEL)

Key Findings: The key finding here is that the number of bathrooms is classified as an ordinal discrete variable because it represents a ranked order (from 1 to 4), and the values are discrete—indicating distinct, separate units without intermediate continuous values. Just as the frequency distribution of the bedroom, this bar chart shows the frequency distribution of the number of bathrooms in the properties. It will also show the range of the numbers of bathrooms most common among the households. This can be useful for comprehension of how the probability of access is divided with concern to the units in the data set.

3. Variable

The number of bathrooms is considered an ordinal discrete variable. This categorization is justified because the variable reflects a ranked order, where each value represents a meaningful progression or quantity of bathrooms. The numbers indicate a clear sequence, from fewer bathrooms to more, which inherently implies an order (ordinal). The values are discrete because they represent distinct, separate units—there are no fractional or continuous numbers between these specified values in this context. While 1.5 or 2.75 bathrooms are possible, the intervals between the listed values are specific and not continuous, further reinforcing the discrete nature of the variable.

4. Histogram of price of Property and land size

Key Findings :This histogram above illustrates the property prices and land sizes. By this, you are able to get a view of how these variables are distributed in that the height of the bars depict the number of properties in the given price or land size category. The shape of the histogram can also reveal whether the data is skewed, normally distributed and whether the data has some other special distribution. Here, the histogram effectively illustrates the distribution and dispersion of the data about property prices and land areas in order to detect the properties such as skewness, peak or any gaps.

5. Descriptive Summary Statistics

Table 2: Descriptive Summary Statistics of price of property
(Source : MS - Excel)

key Findings: The following table provides some of the property price summary measurements which include ‘mean’, ‘median’, ‘standard deviation’ and ‘range’. These measures provide essentials like the central tendencies and variability and also overall appearance of the distribution of property prices in the dataset. Average property price can be calculated using mean and median of the property prices and variability of the prices can be understood through, standard deviation. The range gives the variation of prices from the highest to the lowest, which shows the variation of the values.

Table 3: Descriptive Summary Statistics of Land Size
(Source : MS - Excel)

key Findings : In the same way as with price statistics, the following table gives an overview of some basic descriptive statistics of land size. They include such indicators as the arithmetic average, the median, and the standard deviation because they give a general idea of the size of the land within the established sample. The summary statistics of land size also assist in identifying the degree of dispersion of the land size proportional to properties being analyzed through the mean of the land size and the standard deviation.

6. Normality of the Price of Property Data with Three Pieces of Evidences

Figure 4 : Normality of the price of property Data with three pieces of evidences

(Source : MS EXCEL )

Key Findings:

This, most probably, represents a normality test – Q-Q plot, histogram, or a result of the Shapiro-Wilk test. The purpose is therefore to check the assumption that the property price data can be from a normal distribution. There will be three statistical measures to support or reject normality including histogram of the distribution, measuring the agreement of Q-Q plot and the p-value from a normality test. The condition is that data is normally distributed; it implies that a majority of house prices are exceptionally close to the average while very few prices are on the high or low end. If the data does not look like a normal distribution then further data transformation might be required or analyze the data using other statistical techniques.

7.

Interpretation :

This table gives the confidence interval of the average price of property. The confidence level is usually specified as 95% which means that the true population mean will, in all probability, lie within this range 95% of the time. This interval is important in determining the precision of the sample mean of the population mean. By using confidence intervals to generate hypotheses, it assists in estimating the population mean thus providing a range within which the mean property price lies.

8.

Table 5 : 95 % confidence interval for the population’s average Land Size
(Source : MS - Excel)

As is the case with the property price, this table shows the confidence interval for the average size of the land. It means the mean of the estimated average land size for the population has to be between that range with 95 percent confidence. A small interval provides more accuracy of the estimate as compared with the wide interval.

9.

Table 6: testing of population average price of property
(Source : MS - Excel)

Statistical Decision:

Interpretation: The following table will have the information of whether the null hypothesis should be rejected or not at a significance level (alpha) of 5% using the test statistic and p value. Most often, the p value is determined alongside the lower bound and if the p value gets less than 0. 05, the null hypothesis is being turned down which makes it clear that the average price of the property is significantly different from the set value.

10. Conclusion

This analysis gave a detailed description of property characteristics such as the distribution of the number of bedrooms and bathrooms, the price of the property and land area. These distributions described how frequent a particular combination of bedrooms and bathrooms were and in the analysis, bathrooms was determined to be an ordinal discrete variable because of the ranked and distinct values. Histograms of property prices and size of the land, represented the spread of the corresponding variable and can give an indication of the skewness of the variables. Descriptive statistics yielded measures of central tendency and variability which are important in the assessment of the overall frequency distribution of property prices and sizes of land. The results of the normality tests on property prices indicated that, even though data seemed more or less normally distributed, it was still necessary to conduct additional tests or transformations. The 95% confidence intervals were also employed to estimate the population means of property prices as well as land sizes to show the preciseness of the samples that were taken. Finally, hypothesis testing was used to ascertain whether the mean property price deviated by a statistically significant margin from a given value, in the overall population. Collectively, these analyses provide properties characteristics’ important information and provide practical references for real estate related industries.