Question

When an anthropologist finds skeletal remains, they need to figure out the height of the person. The height of a person (in cm) and the length of their metacarpal bone (in cm) were collected for 19 randomly selected sets of skeletal remains and are in the table below. Test at the 10% level for a positive correlation between length of metacarpal and height for sets of skeletal remains.

length of metacarpal	height
41	162
48	174
46	173
42	165
46	175
43	177
43	170
38	157
47	172
51	180
42	161
50	178
44	171
42	175
49	185
40	155
40	160
48	183
44	173

T: Test Statistic

t = 6.63

O: Obtain the P-value

Report the final answer to 4 decimal places.

It is possible when rounded that a p-value is 0.0000

P-value = 0.0000

M: Make a decision

• Since the p-value ≤_________  , we fail to reject H₀

S: State a conclustion

• There is not is significant evidence to conclude there is a positive linear relation between length of metacarpal and height for all sets of skeletal remains with a length of metacarpal between ___________cm and ___________cm.

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
41	162	11.70	78.18	30.25
48	174	12.81	9.97	11.30
46	173	2.49	4.66	3.41
42	165	5.86	34.13	14.14
46	175	2.49	17.29	6.57
43	177	2.02	37.92	-8.75
43	170	2.02	0.71	1.20
38	157	41.23	191.60	88.88
47	172	6.65	1.34	2.99
51	180	43.28	83.87	60.25
42	161	5.86	96.87	23.83
50	178	31.12	51.24	39.93
44	171	0.18	0.02	-0.07
42	175	5.86	17.29	-10.07
49	185	20.97	200.45	64.83
40	155	19.55	250.97	70.04
40	160	19.55	117.55	47.93
48	183	12.81	147.81	43.51
44	173	0.18	4.66	-0.91

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	844	3246	246.6315789	1346.526	489.263
mean	44.421	170.842	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.849

Ho:   ρ = 0  
Ha:   ρ > 0  
n=   19  
alpha,α =    0.1  
correlation , r=   0.8490  
t-test statistic = r*√(n-2)/√(1-r²) =        6.63

DF=n-2 =   17
p-value =    0.0000

Since the p-value ≤____α=0.10_____  , we reject H₀

There is significant evidence to conclude there is a positive linear