Question

The test statistic of

z= −2.45

is obtained when testing the claim that

p= 2/3.

1.) Using a significance level of

α= 0.05​,

find the critical​ value(s).

Can someone explain how to find the answer step by step without a calculator, I'm Completely lost with the fraction.

Answer 1

Answer)

Our claim is that p = 2/3

So this is a two tailed test.

(As = sign indicates two tailed, < indicates left tailed and > indicates right tailed)

Given alpha = 0.05

Since our test is two tailed, we need to divide the alpha by 2

0.05/2 = 0.025

Now we need to look into the z table,

From z table, p(z<-1.96) = 0.025

And we know that, standard normal z table is symmetrical

So, p(z>1.96) = 0.025

So, required critical values are -1.96 and 1.96

And rejection region is

If test statistics z is less than -1.96 or greater than 1.96

Obtained z is = -2.45

As the obtained z is less than -1.96, it is in the rejection region

So, we reject the null hypothesis.