StatisticsdrillOne-sample z test (σ known)
A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.
The task
A filling machine is set to a mean of 490 grams, and the process standard deviation is known to be σ = 5.5 grams. A random sample of 25 packs has a mean of 491.43 grams. Find the z statistic for H0: μ = 490 against H1: μ ≠ 490, then decide at α = 0.05. Round to 2 decimal places.
What this problem teaches
z = (x̄ - μ0) / (σ / √n). For a two-sided test, reject when |z| is beyond the critical value: 1.645 at α = 0.1, 1.96 at 0.05, 2.576 at 0.01.
A hint if you get stuck
z = (x̄ - μ0) / (σ / √n). For a two-sided test, reject when |z| is beyond the critical value: 1.645 at α = 0.1, 1.96 at 0.05, 2.576 at 0.01.
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