Question

A farmer outside of Clinton NC plants 20 plots of a new type of corn. The average yield for these plots is ī= 150 bushels per acre. Assume that the yield

per acre for the new viety of corn follows a normal distribution with
unknown mean and standard deviation of 20 bushels. Find a 95% confidence
interval.
A. 20 + 3.2
B. 150 +2.5
C. 150 +3.2
D. 150 +4.3

Answer 1

The 95% confidence interval is
`(150\pm 8.8)`.

Explanation:

The information provided is:

`\bar x=150\\\sigma = 20\\n=20`

The critical value for 95% confidence level is:

`z_(\alpha/2)=z_(0.05/2)=z_(0.025)=1.96`

Compute the margin of error as follows:

`MOE=z_(\alpha/2)\cdot(\sigma)/(√(n))`

`=1.96*(20)/(√(20))\\\\=1.96* 4.47214\\\\=8.7653944\\\\\approx 8.8`

Then the 95% confidence interval is:

`CI=\bar x\pm MOE`

`=150\pm 8.8`

Thus, the 95% confidence interval is
`(150\pm 8.8)`.