For σ=12 and n=36 the 95 \% interval for μ is (46.08,\ 53.92). Testing H_0:μ=55 two-sided with α=0.05, what is concluded?

Reject H_0, since 55 lies outside the interval

Do not reject H_0, since 55 is close

Nothing can be said without computing z

Exercise · ZW-HYPOTHESIS-TEST-010 · ★★★ Advanced

For \(\sigma=12\) and \(n=36\) the \(95\,\%\) interval for \(\mu\) is \((46.08,\ 53.92)\). Testing \(H_0:\mu=55\) two-sided with \(\alpha=0.05\), what is concluded?

Choose one option.

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B. Reject \(H_0\), since \(55\) lies outside the interval

Explanation

A two-sided test of level \(\alpha\) rejects \(\mu_0\) exactly when it lies outside the \(1-\alpha\) confidence interval. Here \(55>53.92\).

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Review the concept: Hypothesis test

A hypothesis test is a rule that, from sample data, decides whether to reject the null hypothesis \(H_0\), which fixes a value \(\theta_0\) for a parameter \(\theta\), in favor of the alternative \(H_1\).

\[H_0:\theta=\theta_0\quad\text{versus}\quad H_1:\theta\ne\theta_0\]

For \(\sigma=12\) and \(n=36\) the \(95\,\%\) interval for \(\mu\) is \((46.08,\ 53.92)\). Testing \(H_0:\mu=55\) two-sided with \(\alpha=0.05\), what is concluded?

Explanation

Review the concept: Hypothesis test

More practice problems: hypothesis test