Let [tex]\mu[/tex] be the population mean production of peanuts in Virginia .
As per given , we have
Appropriate hypothesis :
[tex]H_0: \mu=3000\\\\ H_a: \mu>3000[/tex]
Since the alternative hypothesis is right-tailed , so the test is a right-tailed test.
Given : n= 60
[tex]\overline{x}=3120[/tex] pounds of peanuts per acre
[tex]\sigma=578[/tex] pounds of peanuts per acre
Test statistic :
[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z=\dfrac{3120-3000}{\dfrac{578}{\sqrt{60}}}\approx1.61[/tex]
P-value ( For right-tailed test): [tex]P(z>1.61)=0.0536989[/tex]
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.
