Consider the following hypothesis test for the mean differen

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: ?_d = 0 and H_a: ?_d > 0, with n = 23 and t = 1.89.


(b) Determine the p-value for H_o: ?_d = 0 and H_a: ?_d ? 0, with n = 25 and t = -1.8.


(c) Determine the p-value for H_o: ?_d = 0 and H_a: ?_d < 0, with n = 26 and t = -2.51.


(d) Determine the p-value for H_o: ?_d = 0.75 and H_a: ?_d > 0.75, with n = 10 and t = 3.59.

Solution

(a) The degree of freedom =n-1=23-1=22

It is a right-tailed test.

So the p-value= P(t >1.89) =0.0360 (from student t table)

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(b)The degree of freedom =n-1=25-1=24

It is a two-tailed test.

So the p-value= 2*P(t <-1.8) =0.0844 (from student t table)

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(c)The degree of freedom =n-1=26-1=25

It is a left-tailed test.

So the p-value= P(t <-2.51) =0.0095 (from student t table)

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(d)The degree of freedom =n-1=10-1=9

It is a right-tailed test.

So the p-value= P(t >3.59) =0.0029 (from student t table)