Question

Chapters 14 & 170 Help Save & Exit Submit A realtor studies the relationship between the size of a house in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City. [You may find it useful to reference the t table.) 21,805 17,480 Size 2,413 2,401 29,262 2,808 Click here for the Excel Data File 2-1. Calculate the sample correlation coefficiently. (Round to 4 decimal places.) calculations to at least 4 decimal places and final answers Sample correlation coefficient a-2. Interpretiny The correlation coefficient indicates a positive linear relationship. The correlation coefficient indicates a negative linear relationship The correlation coefficient indicates no linear relationship. b. Specify the competing hypotheses in order to determine whether the population correlation coefficient between the size of a house and property taxes differs from zero. < Prey 16 of 30 * Next >

Answer 1

Ans a ) using minitab >stat>basic stat>correlation

we have

Correlation: property taxes, size

Pearson correlation of property taxes and size r_xy= 0.7554
P-Value = 0.000

a 2 ) the correlation coefficient shows a positive linear relationship
b ) $H0:\rho =0$

$H0:\rho \neq 0$

c -1 ) the test statistic t = $\frac{r\sqrt{n-2}}{\sqrt{1-r^{2}}}$

t = $\frac{0.7544\sqrt{20-2}}{\sqrt{1-0.7544^{2}}}$ = 4.876

c-2 ) p value <0.01

d ) do not reject H0, we can state size and property tares are correlated