Question

Exercise 14-4 Algo Consider the following competing hypotheses: H0: ρxy ≥ 0 HA: ρxy < 0 The sample consists of 34 observations and the sample correlation coefficient is –0.58. Use Table 2. a. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic b. Approximate the p-value. p-value < 0.005 0.005 < p-value < 0.01 0.01 < p-value < 0.025 0.025 < p-value < 0.05 c. At the 5% significance level, what is the conclusion to the test? H0, we conclude that the population correlation coefficient between x and y is significantly different from zero. rev: 11_14_2015_QC_CS-31836 References

Answer 1

Hypothesis : H0: ρxy ≥ 0 v\s

HA: ρxy < 0

Left tailed test

Test statistics :

Where , Correlation coefficient = r = -0.58

sample size = n = 34

we get , test statistics = t = -4.0276 .................( ANSWER )

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B ) we want to calculate Pvalue

Pvalue : By using excel we get the exact pvalue

Command is =TDIST(x,DF,tailed)

=TDIST(4.0276,32,1)

=0.0002 ..................( ANSWER )

Therefor Pvalue < 0.005

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C ) Given that ,

Hypothesis :

Ho : x and y are not correlated

v/s   

H1 : x and y are not correlated

Two tailed test

test statistics = t = -4.0276   

Pvalue : By using excel we get the exact pvalue

Command is =TDIST(x,DF,tailed)

=TDIST(4.0276,32,2) = 0.0003

=0.0003 ..................( ANSWER )

Decision Rule : We reject Ho

Conclusion : There is sufficient evidence to conclude that the x and y is significantly different from zero.