Question

Example 2.13 Perform the following hypothesis tests of the population mean. In each case, draw a picture to illustrate the rejection regions on both the Z and X distributions, and calculate the p-value of the test. Ho: μ-25, H,: μ < 25, n . 100, X 24, σ 5, α 0.1

Answer 1

a) H0: $\mu=50$ Ha: $\mu> 50$

Z= 55-5010/sqrt(100)

Z= 5/10/10

Z= 5

Z critical=1.65

P-Value=0.0001 -3 .2 0 test 2 に1 .65

b) Z= 24-25/5/sqrt(100)

Z= -1/5/10

Z= -2

Z critical =-1.28

P-Value=0.0228 .5 .2 test z =-2 -3 -1 0 5

c) Z= 80.5-80/4/sqrt(100)

Z= 0.5/4/10

Z= 0.5*10/4

Z= 1.25

Z c= 1.96

P-Value=0.21 12 -5 -3 .2 0 test z= 1 .25 z= 1 .96