From a large random sample with known σ\sigmaσ, an analyst reports a 95% confidence interval for the population mean:
(12.4, 19.6)(12.4,\ 19.6)(12.4, 19.6)
built as xˉ±1.96⋅SE\bar{x} \pm 1.96 \cdot SExˉ±1.96⋅SE.
Two colleagues now want two-sided z-tests at α=0.05\alpha = 0.05α=0.05 on the same sample:
Which statement is correct?
Select all that apply.
Neither test can be settled from the interval alone — a confidence interval carries no information about hypothesis tests.
H0:μ=20H_0: \mu = 20H0:μ=20 would be rejected only at α=0.10\alpha = 0.10α=0.10, not at α=0.05\alpha = 0.05α=0.05, because 202020 lies just outside the interval.
H0:μ=20H_0: \mu = 20H0:μ=20 is rejected (∣z∣≈2.18|z| \approx 2.18∣z∣≈2.18) while H0:μ=13H_0: \mu = 13H0:μ=13 is not (∣z∣≈1.63|z| \approx 1.63∣z∣≈1.63).
Both are rejected, since neither 202020 nor 131313 equals the point estimate xˉ=16\bar{x} = 16xˉ=16.