Question
Asked Jan 16, 2020
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Sports Diameters (cm), circumferences (cm), and volumes (cm3) from balls used in different sports are listed in the table below. Is there sufficient evidence to conclude that there is a linear correlation between diameters and circumferences? Does the scatterplot confirm a linear association?

Baseball Basketball Golf Soccer Tennis Ping-Pong Volleyball Softball
7.0
20.9
Diameter
21.8
4.0
9.7
7.4
23.9
4.3
65.7
Circumference
68.5
22.0
12.6
30.5
23.2
75.1
13.5
33.5
4780.1
477.9
212.2
7148.1
41.6
179.6
Volume
5424.6
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Baseball Basketball Golf Soccer Tennis Ping-Pong Volleyball Softball 7.0 20.9 Diameter 21.8 4.0 9.7 7.4 23.9 4.3 65.7 Circumference 68.5 22.0 12.6 30.5 23.2 75.1 13.5 33.5 4780.1 477.9 212.2 7148.1 41.6 179.6 Volume 5424.6

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Expert Answer

Step 1

Correlation coefficient:

Null hypothesis: There is no correlation between diameters and circumference.

Alternative hypothesis: There is correlation between diameters and circumference.

The correlation coefficient between the old ratings and new ratings is obtained as 0.9999995 using the EXCEL formula, “=CORREL(A2:A9,B2:B9)”.

Statistics homework question answer, step 1, image 1
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Step 2

T-value:

The value of t-statistic is calculated as given below:

Statistics homework question answer, step 2, image 1
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Step 3

p-value:

Using the EXCEL formula, p-value is obtained as 0.0000 (rou...

Statistics homework question answer, step 3, image 1
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