A statistic equals z=1.7 and is tested at α=0.05. Which statement is correct?

Only the right-tailed test rejects (p=0.0446); the two-sided one does not (p=0.0891)

Both the one-sided and two-sided tests reject H_0

Only the two-sided test rejects

Exercise · ZW-P-VALUE-010 · ★★★ Advanced

A statistic equals \(z=1.7\) and is tested at \(\alpha=0.05\). Which statement is correct?

Choose one option.

Show answer

C. Only the right-tailed test rejects (\(p=0.0446\)); the two-sided one does not (\(p=0.0891\))

Explanation

The one-sided p-value is \(1-\Phi(1.7)=0.0446<0.05\) and the two-sided one is double, \(0.0891>0.05\). The choice of \(H_1\) must be made before seeing the data.

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Review the concept: p-value

The \(p\)-value is the probability \(P\), computed assuming the null hypothesis \(H_0\) is true, of obtaining a result at least as extreme as the one observed.

\[p=P\big(\text{result at least as extreme}\mid H_0\big)\]

A statistic equals \(z=1.7\) and is tested at \(\alpha=0.05\). Which statement is correct?

Explanation

Review the concept: p-value

More practice problems: p-value