Question

The data below shows the selling price​ (in hundred​ thousands) and the list price​ (in hundred​ thousands) of homes sold. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using

alphaαequals=0.05

Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

Selling price (x): 404, 304, 379, 432, 456, 478, 318, 354, 415, 330,

List price (y): 414, 316, 387, 439, 487, 476, 320, 370, 430, 431

What is the null and alternative hypotheses?

Construct a scatterplot of the data:

What is the linear correlation coefficient r?:

What is the test statistic?

What is the p value?:

Is the P value greater or less than the significance level of 0.05 and is there sufficient evidence for a linear correlation between selling price and list price?

Answer 1

Scatter plot of the data.

Using Excel , Enter data in to two columns -----> select all Data -----> click on insert ----> Scatter ----> select first type.

Correlation coefficient r :

Using Excel function , = CORREL( select values x column , select values y column )

r = 0.8734

Hypothesis :

   ,    ( two tailed test )

Where , is population correlation coefficient .

Test statistic :

P-value :

P-value for this two tailed test is ,

P-value = 2* P( t > t_stat ) = 2*P( t > 5.0725 )

Using Excel,    =TDIST( t_stat , df , tail )   , df = n - 2 = 10 - 2 = 8 , tail = 2

=TDIST( 5.0725 , 8 , 2 ) = 0.001

P-value = 0.001

P value is less than the significance level of 0.05 .

Reject null hypothesis.

There is sufficient evidence for a linear correlation between selling price and list price.