Question

A manufacturing company wish to solve a problem in its production line. The production manager develops a hypothesizes test to make sense in general manager’s mind. Production manager use the information below:

The null and alternative hypothesis of

?0: ?=0 versus ?1: ? ≠ 0

A sample correlation of 0.35 for a random sample of size n = 40 (Confidence level is %90).

Test the null hypothesis based on the given information above.

Answer 1

To test the null hypothesis and alternative hypothesis:

H_{​​​​​​0}: The population correlation coefficient is not significantly different from zero.

i.e.H₀: =0

Against

H_{​​​​​​1} : The population correlation coefficient is significantly different from zero.

i.e.H₁: 0

= population correlation coefficient

The given information is:

r= sample correlation coefficient=0.35

n= sample size=40

Test statistic:

Is follow t-distribution with (n-2) degrees of freedom

t=2.3032

Cal | t |= 2.3032

critical value for n-1=40-2=38 degrees of freedom at 10% (i.e. 90% confidence interval) level of Significance is:

tab t= 1.684

P-value at 38 degrees of freedom and 10 % level of Significance is:

p-value =0.02683

Cal | t | > tab t and p-value < 0.10

Therefore,we reject null hypothesis H_{​​​​​​0} at 10% level of Significance.

Conclusion:

There is sufficient evidence to conclude that the population correlation coefficient is significantly different from zero.