Question

The average production of peanuts in Virginia is 3,000 pounds per acre. A new plant food has been developed and is tested on 60 individual plots of land. The mean yeild with the new plant food is 3,120 pounds of peanuts per acre, and the population standard deviation is 578 pounds. Set alpha = 0.04. Can you conclude the average production has increased?

1. State the null hypothesis

2. State the alternative hypothesis

3. Is this a one-tailed test or a tow-tailed test?

4. Find the critical value(s)

5. Compute the test statistic

6. Make the decision (Reject or fail to reject)

7. State the conclusion

Answer 1

1. Null hypothesis

$H_{0}:\mu \leq 300$

2.Alternative hypothesis

$H_{1}:\mu > 300$

3.This is one tailed test

4.Critical value

n=60 Xbar=3120,s=578 alpha=0.04

Critical value =1.7507

5.Test Statistics

$z=\frac{\bar{X}-\mu }{\sigma /\sqrt{n}}=\frac{3120-3000}{578/\sqrt{60}}=1.61$

6.decision:Critical value is greater than calculated value .Fail to reject null hypothesis

7.Conclusion:there is not sufficient evidence to conclude the average production has increased