Question

The average production of peanuts in Virginia is 3000 pounds per acre. A new plant food has been developed and is tested on 60 individual plots of land. The mean yield with the new plant food is 3120 pounds of peanuts per acre, and the population standard deviation is 578 pounds. At α=0.05, can you conclude that the average production has increased?

Answer 1

Answer with explanation:

Let $\mu$ be the population mean production of peanuts in Virginia .

As per given , we have

Appropriate hypothesis  :

$H_0: \mu=3000\\\\ H_a: \mu>3000$

Since the alternative hypothesis is right-tailed , so the test is a right-tailed test.

Given : n= 60

$\overline{x}=3120$ pounds of peanuts per acre

$\sigma=578$ pounds of peanuts per acre

Test statistic :

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$z=\dfrac{3120-3000}{\dfrac{578}{\sqrt{60}}}\approx1.61$

P-value ( For right-tailed test): $P(z>1.61)=0.0536989$

Decision: P-value (0.0536989) is greater than the significance level (0.05), so we fail to reject the null hypothesis.

Conclusion : We conclude that we do not have enough evidence to support the claim that  the average production has increased.