IMathAS-libretexts

To best answer our original question, it might make the most sense to test for significant correlation between income and drawn nickel size. Incomes (in thousands of $) are shown for each of the 75 samples below:

Income (thousands of $)	Coin size (mm)
23	25
23	23
15	21
19	28
20	29
25	25
18	17
12	27
28	22
37	29
22	21
28	29
34	24
25	27
11	24
33	24
35	25
8	19
17	26
29	23
19	25
9	20
31	13
24	29
38	18
15	25
21	26
18	23
34	12
27	26
11	23
18	24
25	22
33	16
20	32
31	15
18	27
20	11
19	29
38	31
56	21
56	19
43	20
88	19
43	26
64	20
64	19
61	19
48	21
75	19
74	13
84	23
42	21
71	17
94	15
100	10
57	19
70	20
87	23
64	18
85	22
87	16
81	15
55	19
47	10
61	23
59	25
98	19
48	20
66	18
42	18
56	28
62	20
95	20
41	14

You can copy the data into Excel by highlighting the data, right-clicking and selecting Copy, then opening Excel, clicking on a blank cell, and selecting Paste from the Edit menu.

Test the claim that there is significant correlation at the 0.05 significance level. Retain at least 3 decimals on all values.

a) If we use

\displaystyle {L}

to denote the low income group and

\displaystyle {H}

to denote the high income group, identify the correct alternative hypothesis.

$\displaystyle {H}_{{1}}:{r}\ne{0}$
$\displaystyle {H}_{{1}}:\mu\ne{0}$
$\displaystyle {H}_{{1}}:\rho={0}$
$\displaystyle {H}_{{1}}:\rho\ne{0}$
$\displaystyle {H}_{{1}}:{p}_{{L}}\ne{p}_{{H}}$

b) The

\displaystyle {r}

test statistic value is:
Hint: You may find it more convenient to use Excel's CORREL, SLOPE, and INTERCEPT functions rather than your calculator

c) The critical value is:
If your sample size falls between table values, use the smaller sample size

d) Based on this, we

Reject $\displaystyle {H}_{{0}}$
Fail to reject $\displaystyle {H}_{{0}}$

e) Which means

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

f) The regression equation (in terms of income

\displaystyle {x}

) is:

\displaystyle \hat{{y}}=

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

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

License

\displaystyle

Income (thousands of $)	Coin size (mm)
23	25
23	23
15	21
19	28
20	29
25	25
18	17
12	27
28	22
37	29
22	21
28	29
34	24
25	27
11	24
33	24
35	25
8	19
17	26
29	23
19	25
9	20
31	13
24	29
38	18
15	25
21	26
18	23
34	12
27	26
11	23
18	24
25	22
33	16
20	32
31	15
18	27
20	11
19	29
38	31
56	21
56	19
43	20
88	19
43	26
64	20
64	19
61	19
48	21
75	19
74	13
84	23
42	21
71	17
94	15
100	10
57	19
70	20
87	23
64	18
85	22
87	16
81	15
55	19
47	10
61	23
59	25
98	19
48	20
66	18
42	18
56	28
62	20
95	20
41	14

Income (thousands of $)	Coin size (mm)
23	25
23	23
15	21
19	28
20	29
25	25
18	17
12	27
28	22
37	29
22	21
28	29
34	24
25	27
11	24
33	24
35	25
8	19
17	26
29	23
19	25
9	20
31	13
24	29
38	18
15	25
21	26
18	23
34	12
27	26
11	23
18	24
25	22
33	16
20	32
31	15
18	27
20	11
19	29
38	31
56	21
56	19
43	20
88	19
43	26
64	20
64	19
61	19
48	21
75	19
74	13
84	23
42	21
71	17
94	15
100	10
57	19
70	20
87	23
64	18
85	22
87	16
81	15
55	19
47	10
61	23
59	25
98	19
48	20
66	18
42	18
56	28
62	20
95	20
41	14

Income (thousands of $)	Coin size (mm)
23	25
23	23
15	21
19	28
20	29
25	25
18	17
12	27
28	22
37	29
22	21
28	29
34	24
25	27
11	24
33	24
35	25
8	19
17	26
29	23
19	25
9	20
31	13
24	29
38	18
15	25
21	26
18	23
34	12
27	26
11	23
18	24
25	22
33	16
20	32
31	15
18	27
20	11
19	29
38	31
56	21
56	19
43	20
88	19
43	26
64	20
64	19
61	19
48	21
75	19
74	13
84	23
42	21
71	17
94	15
100	10
57	19
70	20
87	23
64	18
85	22
87	16
81	15
55	19
47	10
61	23
59	25
98	19
48	20
66	18
42	18
56	28
62	20
95	20
41	14