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The z-test applies when the population standard deviation is known, so the standard error σ/√n needs no estimation. The statistic is compared against the standard normal distribution.
One-sample z
z = (x̄ − μ₀) / (σ/√n)
The standard error is 1.875, so z = 1.8667 and the two-tailed p is about 0.0619 — not significant at 5%.
Rarely in practice, since σ is seldom known. It is also a good approximation to the t-test for large samples.