Question

A hypothesis will be used to test that a population mean equals 10 against the alternative that the population mean is more than 10 with known Ï. What is the critical value of z-score for the following significance levels?
A) 0.01
B) 0.05
C) 0.10

Answer 1

Answer:

A) 2.58

B) 1.96

C) 1.65

Step-by-step explanation:

A hypothesis used to test that

$H_o : \mu = 10$

against the alternatives $H1 : \mu$ not equal to 10

if null hypothesis is true, then distribution of test statics follow

$Zo = \frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}$

for two sided alternatives  hypothesis $( H1: \mu \neq 7)$, then P value is

$P = 2[1- \phi(\left | Zc \right |)]$                          (1)

a)significance level  $\alpha = 0.01$

from 1 eq we get

$\pi (\left | Zc \right |) = P(Zo$

Therefore  $\left | Zc \right | = 2.58$    FROM Z TABLE

B) significance level  $\alpha = 0.05$

from 1st equation we get

$\pi (\left | Zc \right |) = P(Zo < \left | Zc \right |) = 1 - \frac{0.05}{2} = 0.975$

Therefore  $\left | Zc \right | = 1.96$    FROM Z TABLE

C) significance level  $\alpha = 0.10$

from 1 eq we get

$\pi (\left | Zc \right |) = P(Zo$

Therefore  $\left | Zc \right | = 1.65$    FROM Z TABLE