Question

The test statistic of zequalsnegative 2.01 is obtained when testing the claim that pless than0.18. a. Using a significance level of alphaequals0.05​, find the critical​ value(s). b. Should we reject Upper H 0 or should we fail to reject Upper H 0​?

Answer 1

(a) The critical​ value is -1.64.

(b) We fail to reject the null hypothesis H₀.

Explanation:

(a)

The test statistic of z=-2.01 is obtained when testing the claim that p<0.18. It means the data belongs to normal distribution.

Null hypothesis:

`H_0:p\geq 0.18`

Alternative hypothesis:

`H_1:p<0.18`

It is left tailed test.

Using a significance level of α=0.05​ we need to find the critical​ value.

From the standard normal table the critical value at α=0.05 for left tailed is -1.64.

Therefore the critical​ value is -1.64.

(b)

If z > critical value, then we reject the null hypothesis.

If z < critical value, then we fail to reject the null hypothesis.

In the given problem z=-2.01 and critical value = -1.64.

`-2.01<-1.64\Rightarrow z<\text{critical value}`

Since z < critical value, therefore we fail to reject the null hypothesis H₀.