Respuesta :
Answer:
As [tex]Z<-Z_{\alpha}[/tex], it is possible to reject null hypotesis. It means that the local mean height is less tha 0.7 m with a 5% level of significance.
Step-by-step explanation:
1. Relevant data:
[tex]\mu=0.70\\N=40\\\alpha=0.05\\X=0.65\\s=0.20[/tex]
2. Hypotesis testing
[tex]H_{0}=\mu=0.70[/tex]
[tex]H_{1} =\mu< 0.70[/tex]
3. Find the rejection area
From the one tail standard normal chart, whe have Z-value for [tex]\alpha=0.05[/tex] is 1.56
Then rejection area is left 1.56 in normal curve.
4. Find the test statistic:
[tex]Z=\frac{X-\mu_{0} }{\sigma/\sqrt{n}}[/tex]
[tex]Z=\frac{0.65-0.70}{0.20/\sqrt{40}}\\Z=-1.58[/tex]
5. Hypotesis Testing
[tex]Z_{\alpha}=1.56\\Z=-1.58[/tex]
[tex]-1.58<-1.56[/tex]
As [tex]Z<-Z_{\alpha}[/tex], it is possible to reject null hypotesis. It means that the local mean height is less tha 0.7 m with a 5% level of significance.
