Question

The null and alternative about hypotheses a normal population N (μ, σ^2) is H0， μ=21 , H1: μ<21. Choose a sample of size n=17 with X(average)= 23 and S^2 = (3.98)^2. The statistic we should use is____, the size of the lest. α=0.05 , and the result of the test is____H0.

Answer 1

(a)

H0: Null Hypothesis: = 21

H1: Alternative Hypothesis: < 21

SE = s/

= 3.98/

= 0.9653

Test Statistic is given by:

t = (23 - 21)/0.9653

= 2.0719

So,

Answer is:

t = 2.0719

(b)

= 0.05

ndf = n - 1 = 17 - 1 = 16

One Tail - Left Side Test

From Table, critical value of t = - 1.7459

Since calculated value of t = 2.0719 is greater than critical value of t = - 1.7459, the difference is not significant. Fail to reject null hypothesis.

So,

Answer is:

Fail to reject H0.