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Question

# The test statistic of z = 2.01 is obtained when testing the claim that $p \ne 0.345$. Using a significance level of $\alpha$ = 0.05, should we reject $H_0$ or should we fail to reject $H_0$ ?

Solution

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Given:

$z=2.01$

$\alpha=0.05$

Given claim: $p\neq 0.345$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis and the alternative hypothesis state the opposite of each other. The null hypothesis needs to contain an equality.

$H_0:p=0.345$

$H_0:p\neq 0.345$

The critical values are the values corresponding to a probability of $\alpha/2=0.025$ and $1- \alpha/2=0.975$ in the normal probability table in the appendix:

$z=\pm 1.96$

The rejection region then contains all values below $-1.96$ and all values above 1.96.

If the value of the test statistic is within the rejection region, then the null hypothesis is rejected:

$2.01>1.96\Rightarrow \text{ Reject } H_0$

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