Question

The data below shows the selling price​ (in hundred​ thousand) and the list price​ (in a hundred​ thousand) 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)	400400	305305	376376	433433	455455	477477	315315	355355	416416	331331
List Price​ (y)	414414	317317	385385	440440	489489	479479	325325	367367	433433	342342

What are the null and alternative​ hypotheses?

A. H0​: rhoρequals=0 H1​: rhoρgreater than>0

B. H0​: rhoρequals=0 H1​: rhoρnot equals≠0

C. H0​: rhoρnot equals≠0 H1​: rhoρequals=0

D. H0​: rhoρequals=0 H1​: rhoρless than<0

Construct a scatterplot. Choose the correct graph below.

A.  A scatterplot has a horizontal x-scale from 300 to 500 in intervals of 20 and a vertical y-scale from 300 to 500 in intervals of 20. Ten points are plotted with approximate coordinates as follows: (305, 315); (315, 325); (330, 340); (355, 365); (375, 385); (400, 415); (415, 435); (435, 440); (455, 490); (475, 480).

B.  A scatterplot has a horizontal x-scale from 300 to 500 in intervals of 20 and a vertical y-scale from 300 to 500 in intervals of 20. Eleven points are plotted with approximate coordinates as follows: (305, 485); (330, 340); (350, 465); (360, 405); (390, 400); (400, 475); (410, 375); (415, 435); (430, 355); (430, 400); (455, 460).

C.  A scatterplot has a horizontal x-scale from 300 to 500 in intervals of 20 and a vertical y-scale from 300 to 500 in intervals of 20. Ten points are plotted with approximate coordinates as follows: (305, 330); (315, 370); (355, 415); (365, 350); (410, 450); (415, 380); (420, 425); (465, 485); (470, 405); (470, 455).

D.​​​​​​​ It won't let me copy and paste it but it is going down from the top left to the bottom right of the graph

The linear correlation coefficient r is:

​(Round to three decimal places as​ needed.)

The test statistic t is:
​(Round to three decimal places as​ needed.)

The​ P-value is:

​(Round to three decimal places as​ needed.)

Because the​ P-value is (less/ greater) than the significance level 0.05, there (is not/ is) sufficient evidence to support the claim that there is a linear correlation between selling price​ (in hundred​ thousand) and the list price​ (in hundred​ thousand) of homes sold for a significance level of alphaαequals=0.05

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable: y Independent Variable: x y = 3.4470205 + 1.0242117 x Sample size: 10 R (correlation coefficient) 0.99080191 R-sq 0.98168843 Estimate of error standard deviation: 8.8517047 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 3.4470205 19.308896 # 0 8 0.17851981 0.8628 Slope 1.0242117 0.04945619 # 0 8 20.709475 0.0001

Hence,

Hypotheses: H0​: ρ=0 H1​: ρ≠0

Option B is correct.

Scatterplot: Option A is correct.

r = 0.991

t = 20.709

P = 0.000

Less; is