PART A
(a) Using the sample data attached for all three suburbs, calculate the sample mean and sample standard deviation for the variables:
i. Appraised value (000's $)
ii. House Size (sq.ft)
iii. Age (in years)
iv. Land Acreage
Provide excel spreadsheet showing all calculations clearly
Provide adequate formulas used in this question
(b) Are any of the variables in the data set categorical in nature? If so which ones?
(c) Is there any evidence of skewness in these data sets? Which data set(s) display positive skewness and which ones negative skewness? Which data set is least skewed? In answering this question you should use the appropriate statistic (Pearson's coefficient of skewness), and not simply the skewness measure generated in the PHStat4 output.
(d) Check for normality for the following variables
i. House Size (sq.ft)
ii. Age (in years)
Use the PHStat normal probability plot. Comment on your calculation. Include the plots in your submission
(e) You now are told that from analysis of past data, the variable age for GLEN COVE homes has followed a normal distribution. From past experience you know that the population mean age of the home was 50 years and a standard deviation of 20 years. If you select an individual company from this population (not from your sample) determine the probability that the age of the home is:
(i) Less than 40 years
(ii) Between 40 and 45 years
(iii) Now assuming you take a random sample of 100 homes in the GLEN COVE area from the population described in the paragraph above, what is the probability that the sample mean Age for these homes would have a mean age is less than 45 years?
(f) Using the sample data on Appraised value ($) for GLEN COVE ONLY, what is the sample proportion and its standard deviation of Appraisals whose value ($) is less than 300.
(g) Set up and interpret the following confidence intervals:
Use the decision tree diagram to justify your choice of distribution in answering the above questions.
(i) a 95% confidence interval for the true population mean house size for all suburbs
(ii) a 99% confidence interval for the true population mean Age of the home for all suburbs
(iii) a 90% confidence interval to estimate the true population proportion of appraisals whose value ($) is less than 300
(h) A follow-up study will provide a point estimate of the population proportion of Appraisals whose values ($) are less than 300. The study must provide 90% confidence that the point estimate is within 0.10 of the population proportion. If no previous proportion estimate is available, how large a sample would you recommend for this study?
PART B
Using the computer software package PHStat and Excel Data Analysis, confirm your answers with the appropriate printout attached for the following parts from PART A.
(a) Using the Descriptive Statistics function of Excel Data Analysis, print the complete computer output for all statistics for all four variables from part A (a)
(b) Use PhStat to confirm you answers in part A (e)
(c) Use PhStat to print all confidence intervals computer outcomes from Part A (g)
(d) Use PhStat to print the sample size computer outcome in Part A (h)