Statistics using R A data set describing the sale of individual residential prop

Question

Statistics using R

A data set describing the sale of individual residential property in Ames, Iowa from 2006 to 2010 was obtained by Dean De Cock, a statistics professor at Truman State University. The data set contains 2930 observations and a large number of explanatory variables involved in assessing home values. Source: http://www.amstat.org/publications/jse/v19n3/decock.pdf

We will look at a sample of 200 homes from this data set. These homes are all located in the Sawyer neighborhood of the city. Observations include the following eight variables:
• lot_shape: Lot Shape
o Reg = Regular
o IRR = Irregular
• lot_config: Lot configuration
o Inside = Inside lot
o Corner = Corner lot
• Style
o Yes = Home has one story
o No = Home has more than one story
• roof_style: Type of Roof
o Gable = Gable
o Hip = Hip
• garage_area : Size of garage in square feet
• lot_area: Lot size in square feet
• living_area: Total home living area in square feet (including unfinished square footage)
• sale_price: Sale price in dollars

Access the data for this problem using the command sawyer<-read.csv("http://www.math.usu.edu/cfairbourn/Stat2300/RStudioFiles/data/sawyer.csv")
Instructions

Watch the video demonstrating how to conduct hypothesis tests in RStudio. For the question below, include your R code and the output.

1. The mean living area in square feet for all residential properties in Ames, Iowa is 2547 square feet. Use R to conduct a hypothesis test to determine if the mean above grade living area for homes in the Sawyer neighborhood is significantly different from 2547 square feet. State your null and alternative hypotheses, your R output, and your conclusion based on the strength of the evidence.

Explanation / Answer

The R snippet is as follows

sawyer<-read.csv("http://www.math.usu.edu/cfairbourn/Stat2300/RStudioFiles/data/sawyer.csv")

## perform the t test

t.test(sawyer$living_area, mu = 2547, alternative = "two.sided")

#########

The results are

> t.test(sawyer$living_area, mu = 2547, alternative = "two.sided")

   One Sample t-test

data: sawyer$living_area
t = -5.9173, df = 199, p-value = 1.41e-08 , as the p value is less than 0.05 , hence we reject the null hypothesis in favor of alternate hypothesis
alternative hypothesis: true mean is not equal to 2547
95 percent confidence interval:
2233.946 2390.444
sample estimates:
mean of x
2312.195

H0 : the mean of living area is not different from 2547

H1 : the mean of living area is statisitcally different from 2547

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