Does the new fertilizer raise yield above 170 bushels?

Question

The standard corn yield is 170 bushels per acre with a known standard deviation of $\sigma = 20$ . A company claims its new fertilizer raises the mean yield. A trial on 25 plots gives a mean of 178 bushels.

Run a one-sided z-test at the 5% level (does yield increase?): report the z-statistic and the decision.

Accepted Answer

The claim is directional (yield goes up), so use an upper-tail one-sided test. Because \sigma is known, use a z-test. Hypotheses: H0: \mu = 170 versus H1: \mu 170. Standard error: 	ext{SE} = \frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{25}} = \frac{20}{5} = 4. Test statistic: z = \frac{178 - 170}{4} = \frac{8}{4} = 2.0. The one-sided 5% critical value is z{0.05} = 1.645. Since 2.0 1.645, reject H0. The one-sided p-value is 1 - \Phi(2.0) = 0.0228. Conclusion: there is evidence the fertilizer increases mean yield. Takeaway. A one-sided test spends the full 5% in the upper tail, so the cutoff (1.6…

Does the new fertilizer raise yield above 170 bushels?

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