Question

Crop researchers are interested in the productivity of a new variety of corn. They plant 25 plots with randomly selected seeds of the new variety, record the yield in bushels per acre, and find that a 99% confidence interval for the true mean yield is 118 to 130 bushels per acre.
(a) Interpret the confidence interval
(b) What is the point estimate that was used to create the interval? What is the margin of error?
Show your work
(c) Interpret the confidence level
(d) Based on the research, a marketer tells a possible customer that with this new variety of com they can expect to receive more than 130 bushels per acre, on average. Use the confidence interval to evaluate this statement.

Answer 1

Answer:

a) The CI has  the information of the range of values for the numbers of bushels per acre to get with the new seeds

b) 124     MOE = 6

c) The confidence level is for  α = 1%  α /2 = 0,5%   α /2 = 0,005

its interpretation is associated to CI

d) With that information, we can´t tell customers that the new variety of seeds, they can expect to receive more than 130 bushels per acre on average

Step-by-step explanation:

a) The number of bushels per acre with the selected seeds will be between the values 118 up to 130 with a 99% of confidence

Confidence Interval   CI = 99 %    then  significance level is α = 1%

or    α  =  0,01 ,  with  sample size  25    degree of freedom is 24, then from t-student table we find   t (c)  =  2,797

We also know that in order to get   CI ( 118 , 130 )

Note:CI interval is symmetric about the middle point (which is the mean )

(118 + 130 )/2  =  124

So    CI =  (  124 -6  ;  124 + 6 )

CI =  ( μ₀  -  MOE  ;  μ₀  +  MOE )

Then MOE = 6

With that information, we can´t tell customers that the new variety of seeds, they can expect to receive more than 130 bushels per acre on average

Answer 2

In this exercise we have to use the knowledge of probability to identify the confidence level and the interval, in this way we have:

a) The CI is the range of values for the numbers of bushels per acre to get with the new seeds.

b) 124     MOE = 6

c)  α = 1%  α /2 = 0,5%   α /2 = 0,005

d) 130 bushels per acre on average

Now we have to first identify the confidence level as:

$CI = 99 \% \\\alpha = 1\% \ or \ \alpha = 0,01 \\ t (c) = 2,797$

Now calculating the confidence interval as:

$(118 + 130 )/2 = 124\\CI = ( 124 -6 ; 124 + 6 )\\CI = ( \mu_o - MOE ; \mu_0 + MOE )\\MOE = 6$

See more about probability at brainly.com/question/795909