Consider the following competing hypotheses and accompanying sample data. Use Table 8. |
H_{0}: ?_{S} = 0 |
H_{A}: ?_{S} ? 0 |
r_{S} = 0.71 and n = 9 |
a-1. |
Determine the critical value at the 1% significance level. (Round your answer to 3 decimal places.) |
Critical value |
b. |
What is the value of the test statistic? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) |
Test statistic |
we have n = 9, so degree of freedom = n-2 = 9-2 = 7
correlation coefficient is r = 0.71
(A) Using the student's t distribution table with degree of freedom 7 and significance level 0.01, we get t critical value = 3.499 (rounded to three decimals)
(B) calculation for t statistic
t statistic =
setting n = 9 and r= 0.71
this gives
t statistic =
so, the test statistic t = 2.67 (rounded to two decimals)
Since the t statistic is less than t critical, thus we fail to reject the null hypothesis.
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