Answer to Question #158846 in Statistics and Probability for rr

Question #158846

A farmer is trying out a planting technique that he hopes will increase the yield on his pea plants. The average number of pods on one of his pea plants is 145 pods with a standard deviation of 100 pods. This year, after trying his newplanting technique, he takes a random sample of 144 his plants and finds the average number of pods to be 147. Do the data provide sufficient evidence, at α=0.05, to conclude that the new planting technique is effective in increasing yield?


1
Expert's answer
2021-02-02T04:18:28-0500

H0: μ≤145

H1: μ>145

Z=xˉμσ/n=147145100/144=0.24Z = \frac{\bar{x}-μ}{σ/ \sqrt{n}} \\ = \frac{147-145}{100/ \sqrt{144}} \\ = 0.24

At α=0.05 the critical value will be 1.64 (By using e-calculator https://www.calculators.org/math/z-critical-value.php).

The value of the test statistics is 0.24 < 1.64. So, we accept the null hypotheses and conclude that the new planting technique is not effective in increasing yield.


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