Answer:
99% confidence interval for the true mean yield is [46.718 , 52.482].
Step-by-step explanation:
We are given that a random sample of 8 fields of barley has a mean yield of 49.6 bushels per acre and standard deviation of 2.33 bushels per acre.
Firstly, the pivotal quantity for 99% confidence interval for the true mean yield is given by;
P.Q. = ~
where, = sample mean yield = 49.6 bushels per acre
s = sample standard deviation = 2.33 bushels per acre
n = sample of fields of barley = 8
= true population mean
<em>Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.</em>
So, 99% confidence interval for the true mean, is ;
P(-3.499 < < 3.499) = 0.99 {As the critical value of t at 7 degree of
freedom are -3.499 & 3.499 with P = 0.5%}
P(-3.499 < < 3.499) = 0.99
P( <
<
) = 0.99
P( <
<
) = 0.99
<u>99% confidence interval for</u> = [
,
]
= [ ,
]
= [46.718 , 52.482]
Therefore, 99% confidence interval for the true mean yield is [46.718 , 52.482].