Answer to Question #113940 in Statistics and Probability for Jack

Question

An agriculturists is trying out a planting technique that he hopes will increase the yield on his orange plants. The average number of pods on one of his orange plants is 118 pods with a standard deviation of 80 pods. This year, after trying his new planting technique, he takes random sample of his plants and fins the average number of pods to be 125. He wonders whether or not this is a statistically significant increase. What are his hypotheses and the test statistic? Use a 0.05 significance level.

Answer 1

$Ho: \mu=118$

$Ha: \mu>118$

$Z=\frac{\bar{x-\mu}}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{125-118}{\frac{80}{\sqrt{1}}}=0.0875$

$Z(0.05)$ right tailed is 1.645.

Since 0.0875 is less than 1.645, we fail to reject the null hypothesis and conclude that the increase is not significant.