Question

Suppose that you are testing the following hypotheses where the variance is unknown: H0 : µ = 100 H0 : µ ≠ 100 The sample size is n 20. Find bounds on the P-value for the following values of the test statistic. a. t0 = 2.75 b. t0 = 1.86 c. t0 = -2.05 d. t0 = -1.86

Answer 1

Solution

The null and alternative hypothesis is ,

H₀ :   = 100

H_a :    100

n = 20

degrees of freedom = n - 1 = 20 - 1 = 19

This is the two tailed test .

a) t0 = 2.75

P(t > 2.75) = 1-P (t < 2.75) = 1 - 0.9936 = 0.0064

P-value = 2 * P(t > 2.75)

P-value = 2 * 0.0064

P-value = 0.0128

b) t0 = 1.86

P(t > 1.86) = 1-P (t < 1.86) = 1 - 0.9608 = 0.0392

P-value = 2 * P(t > 1.86)

P-value = 2 * 0.0392

P-value = 0.0784

c) t0 = -2.05

P(t < -2.05) = 0.0272

P-value = 2 * P(t < -2.05)

P-value = 2 * 0.0272

P-value = 0.0544

d) t0 = -1.86

P(t < -1.86) = 0.0392

P-value = 2 * P(t < -1.86)

P-value = 2 * 0.0392

P-value = 0.0784