Question

# Consider the following competing hypotheses and accompanying sample data. Use Table 8. H0: ?S = 0...

 Consider the following competing hypotheses and accompanying sample data. Use Table 8.
 H0: ?S = 0 HA: ?S ? 0 rS = 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.