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Question

# The test statistic of z = 2.01 is obtained when testing the claim that $p \ne 0.345$. Find the P-value.

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 P-value is the probability of obtaining the value of the test statistic, or a value more extreme, when the null hypothesis is true. Determine the P-value using the normal probability table in the appendix.

$P=P(Z<-2.01\text{ or }Z>2.01)=2P(Z<-2.01)=2(0.0222)=0.0444$

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