Determine the bounds on the pvalue that would be used in tes

Determine the bounds on the p-value that would be used in testing each of the following null hypotheses using the p-value approach.

(a)

H₀: = 0 vs. H_a: 0,

with n = 47 and r = 0.37
? < P <?

(b)

H₀: = 0 vs. H_a: > 0,

with n = 10 and r = 0.716
P = ?

(c)

H₀: = 0 vs. H_a: < 0,

with n = 15 and r = -0.88
P <?

Solution

(a)

H₀: = 0 vs. H_a: 0,

with n = 47 and r = 0.37

t = r / sqrt((1-r^2)/(n-2))

= 0.37/ sqrt((1-(0.37)^2)/(47-2))

= 2.67

P -value = 2 (1-0.9962) = 0.0076 Answer

(b)

H₀: = 0 vs. H_a: > 0,

with n = 10 and r = 0.716
t = r / sqrt((1-r^2)/(n-2))

= 0.716/ sqrt((1-(0.716)^2)/(10-2))

= 2.9

P -value = (1-0.9981) = 0.0019 Answer
(c)

H₀: = 0 vs. H_a: < 0,

with n = 15 and r = -0.88
t = r / sqrt((1-r^2)/(n-2))

= -0.88/ sqrt((1-(-0.88)^2)/(15-2))

= -6.68

P -value ~ 0 Answer