Question

Consider the following hypothesis test for the mean difference. (Give your answers correct to four decimal places.)

(a) Determine the p-value for H_o: μ_d = 0 and H_a: μ_d > 0, with n = 19 and t = 1.99.


(b) Determine the p-value for H_o: μ_d = 0 and H_a: μ_d ≠ 0, with n = 19 and t = -1.93.


(c) Determine the p-value for H_o: μ_d = 0 and H_a: μ_d < 0, with n = 25 and t = -2.58.


(d) Determine the p-value for H_o: μ_d = 0.75 and H_a: μ_d > 0.75, with n = 7 and t = 3.58

Answer 1

(a)

Right tailed test :

Degrees of freedom = n-1 =19-1=18

Test statistic : t_stat=1.99

For 18 degrees of freedom , P(t>1.99) = 0.031

p-value = 0.031

(b)

Two tailed test :

n = 19 and t = -1.93

Degrees of freedom = n-1 =19-1=18

For Two tailed test:

For 18 degrees of freedom , P(t>1.93) = 0.03475

p-value = 0.0695

(c)

Left tailed test:

n = 25 and t = -2.58.

Degrees of freedom = n-1=25-1=24

For 24 degrees of freedom,

P(t>-2.58) = 0.9918 ; P(t<-2.58) = 1-P(t>-2.58) = 1-0.9918=0.0082

p-value = 0.0082

(d)

Right tailed test:

n = 7 and t = 3.58

Degrees of freedom = n-1 = 7-1=6

for 6 degrees of freedom, P(t>3.58) = 0.0058

p-value = P(t>3.58) = 0.0058

p-value = 0.0058