A random sample of 75 pre-school children was taken. The childwas asked to draw a nickel. The diameter of that nickel wasrecorded. Their parent's incomes (in thousands of $) and thediameter of the nickel they drew are given below.

Income (thousands of $)	Coin size (mm)
25	23
16	24
11	25
30	22
36	19
18	28
27	31
28	24
34	21
27	24
14	25
13	20
37	21
17	18
36	25
12	21
10	20
25	26
27	20
34	27
26	26
21	19
9	25
21	22
17	21
14	26
25	21
14	13
38	16
38	16
36	19
27	20
33	14
18	14
28	19
8	15
31	17
33	13
39	21
36	22
59	25
64	20
52	20
90	20
54	14
92	18
41	22
68	23
84	23
48	23
67	23
51	22
86	17
42	18
63	20
94	12
82	20
40	20
46	16
40	21
54	21
98	18
97	15
46	16
49	21
85	30
81	23
84	23
64	16
56	21
66	21
65	24
73	13
42	26
84	14

Test the claim that there is significant correlation at the0.01 significance level. Retain at least 3decimals on all values.

a) Identify the correct alternative hypothesis.

• H1:ρ=0H1:ρ=0
• H1:r≠0H1:r≠0
• H1:μ≠0H1:μ≠0
• H1:pL≠pHH1:pL≠pH
• H1:ρ≠0H1:ρ≠0

b) The rr test statistic value is:   

c) The critical value is:

d) Based on this, we

• Reject H0H0
• Fail to reject H0H0

e) Which means

• There is sufficient evidence to warrant rejection of theclaim
• There is not sufficient evidence to support the claim
• The sample data supports the claim
• There is not sufficient evidence to warrant rejection of theclaim

f) The regression equation (in terms of income xx) is:
ˆy=y^=   

g) To predict what diameter a child would draw a nickel givenfamily income, it would be most appropriate to:

• Use the regression equation
• Use the mean coin size
• Use the P-Value
• Use the residual