input data
data= read.csv("C:\\Users\\69412\\Desktop\\Housing_prices.csv")
head(data)
##   ID river  rooms price  age industry ptratio low_ses
## 1  1    No 6-room  21.6 78.9     7.07    17.8    9.14
## 2  2    No 7-room  34.7 61.1     7.07    17.8    4.03
## 3  3    No 7-room  33.4 45.8     2.18    18.7    2.94
## 4  4    No 7-room  36.2 54.2     2.18    18.7    5.33
## 5  5    No 6-room  28.7 58.7     2.18    18.7    5.21
## 6  6    No 6-room  20.4 61.8     8.14    21.0    8.26

####Present the study design, null and alternative hypotheses (5%) Study Design: The study is designed to analyze the relationship between the number of rooms in a house and the house’s price within a given dataset. This will be done through descriptive statistics, visualization, and inferential statistics. Null Hypothesis (H0): There is no significant difference in housing prices among houses with different numbers of rooms. Alternative Hypothesis (H1): There is a significant difference in housing prices among houses with different numbers of rooms. #### Describe the characteristics of the study sample by the number of rooms/house (10%)

dim(data)
## [1] 372   8
summary(data$rooms)
##    Length     Class      Mode 
##       372 character character

Develop and interpret a histogram for the distribution of house prices (10%) or use ggplot2

hist(data$price, main = "Distribution of House Prices", xlab = "price", breaks = 30, col = "green")

#### Develop and interpret a box plot to describe the differences in housing prices among the number of rooms per household (10%) can use ggplot2

boxplot(data$price ~ data$rooms, main = "Housing Prices by Number of Rooms", xlab = "Number of Rooms", ylab = "Price", col = "lightblue")

##### Conduct a statistical test to determine whether housing prices were different among houses with different numbers of rooms. Interpret the findings (15%)

anova_test= aov(price ~ rooms, data = data)
summary(anova_test)
##              Df Sum Sq Mean Sq F value Pr(>F)    
## rooms         3   7162  2387.2   43.49 <2e-16 ***
## Residuals   368  20202    54.9                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Determine which particular number of rooms/house had different house prices using the Tukey posthoc test. Fill in the following table and interpret the findings (20%)

tukey_result = TukeyHSD(anova_test)
tukey_result
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = price ~ rooms, data = data)
## 
## $rooms
##                    diff       lwr       upr     p adj
## 5-room-4-room -3.215556 -9.373321  2.942210 0.5331459
## 6-room-4-room  1.603780 -3.477109  6.684668 0.8475492
## 7-room-4-room 11.511053  6.108559 16.913546 0.0000004
## 6-room-5-room  4.819335  0.948716  8.689954 0.0077590
## 7-room-5-room 14.726608 10.442544 19.010672 0.0000000
## 7-room-6-room  9.907273  7.407162 12.407384 0.0000000