An agricultural researcher plants 25 plots with a new variety of yellow corn.Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with an unknown mean of $\mu$ and a standard deviation of $\sigma$ = 10 bushels per acre.If the average yield for these 25 plots is = 150 bushels per acre,what is a 90% confidence interval for $\mu$?
A)150 ± 0.784
B)150 ± 2.00
C)150 ± 3.29
D)150 ± 3.92

Question

An agricultural researcher plants 25 plots with a new variety of yellow corn.Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with an unknown mean of $\mu$ and a standard deviation of $\sigma$ = 10 bushels per acre.If the average yield for these 25 plots is  = 150 bushels per acre,what is a 90% confidence interval for $\mu$?
A)150 ± 0.784 
B)150 ± 2.00 
C)150 ± 3.29 
D)150 ± 3.92

Quizplus · Accepted Answer

We use the formula for the confidence interval for the mean:

CI = x̄ ± z* (σ/√n)

where x̄ = 150 (sample mean), σ = 10 (population standard deviation), n = 25 (sample size), and z* is the critical value for a 90% confidence level, which is 1.645 (from a standard normal distribution table).

Substituting the values, we get:

CI = 150 ± 1.645 * (10/√25) = 150 ± 3.29

Therefore, the 90% confidence interval for the population mean yield is 150 ± 3.29 bushels per acre. The closest answer choice is (C).

An Agricultural Researcher Plants 25 Plots with a New Variety μ\muμ

An Agricultural Researcher Plants 25 Plots with a New Variety $\mu$