SOLUTION: An urban sociologist interested in neighborliness collected data for a sample of 10 adults on (X) how many years they have lived in their neighborhood and (Y) how many of their nei

Question 86927This question is from textbook elementary statistics in social research
: An urban sociologist interested in neighborliness collected data for a sample of 10 adults on (X) how many years they have lived in their neighborhood and (Y) how many of their neighbors they regard as friends. Compute a Pearson's correlation coefficient for these data and determine whether the correlation is significant.
X Y
________
1 1
5 4
6 2
1 3
8 5
2 1
5 2
9 6
4 7
2 0
________This question is from textbook elementary statistics in social research

Answer by stanbon(48568) (Show Source):
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An urban sociologist interested in neighborliness collected data for a sample of 10 adults on (X) how many years they have lived in their neighborhood and (Y) how many of their neighbors they regard as friends. Compute a Pearson's correlation coefficient for these data and determine whether the correlation is significant.
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Using the TI-83 Linear Regression program I get an r value of 0.61
which indicates weak positive linear correlation.
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Hypothesis Test Setup:
Ho: rho = 0 (meaning there is no linear correlation)
Ha: rho is not equal to 0 (meaning there is some linear correlation)
Using a Pearson Product-Moment Correlation Coefficient Table
you find (for 10-2 degrees of freedom) the critical value is 0.632
for a two-tailed ted with alpha=5%.
Since 0.61 (the test statistic) is not greater than 0.632 you fail to
reject Ho; you conclude this test did not show significant statistic
evidence of strong linear correlation in the data.
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Cheers,
Stan H.