Question

please answer both with an explanation

(14) For testing Ho : µ1 = µ2 versus H1 : µ1 # µ2, a completely randomized design used two indpendent samples of sizes n = m = 10 and obtained t-statistics = -2.87. If the assumption of equal but unknown population variances is justified, what is the p-value? The following "answers" have been proposed. (a) Approximately 0.005 (b) Approximately 0.01 (c) Approximately 0.025 (d) Approximately 0.05 (e) None of the above. The correct answer is (a) (b) (c) (d) N/A (Select One) (15) For testing Ho : Hi SH2 versus H1 : H1 > µ2, a matched pairs design used samples n = m = 10 obtained t-statistic = 2.87, where the larger the statistic the more the evidence against the null hypothesis. What is the p-value? The following "answers" have been proposed. (a) Approximately 0.005 (b) Approximately 0.01 (c) Approximately 0.025 (d) Approximately 0.05 (e) None of the above. The correct answer is (a) (b) N/A (Select One)

Answer 1

14)

Degrees of freedom = n + m - 1 = 10 + 10 - 1 = 19

t value = -2.870

Two tailed test

We need to find the corresponding probability (p)

Use the function =T.DIST.2T(2.87,19) in excel it will give the two tailed p value. ( although the value is -2.87 but in two tail | -2.87 | = 2.87 is used.

p = 0.0098

b) Approximately 0.01

15)

Degrees of freedom = n + m - 1 = 10 + 10 - 1 = 19

t value = -2.870

One tailed test

We need to find the corresponding probability (p)

Use the function =T.DIST(-2.87,19,TRUE) in excel it will give the one tailed p value..

p = 0.0049

a) Approximately 0.005