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Question

The test statistic of z = 2.01 is obtained when testing the claim that p0.345p \ne 0.345. Using a significance level of α\alpha = 0.05, should we reject H0H_0 or should we fail to reject H0H_0 ?

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Given:

z=2.01z=2.01

α=0.05\alpha=0.05

Given claim: p0.345p\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.

H0:p=0.345H_0:p=0.345

H0:p0.345H_0:p\neq 0.345

The critical values are the values corresponding to a probability of α/2=0.025\alpha/2=0.025 and 1α/2=0.9751- \alpha/2=0.975 in the normal probability table in the appendix:

z=±1.96z=\pm 1.96

The rejection region then contains all values below 1.96-1.96 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 Reject H02.01>1.96\Rightarrow \text{ Reject } H_0

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