Homework Sourseplease show all work thank you An agronomist measured the he
please show all work. thank you!
An agronomist measured the heights of 100 corn plants in Iowa. Within his sample, he found that the mean height was 220 cm and the standard deviation was 15 cm. (a) State in words the population mean of this problem. (b) Construct a 95% confidence interval for the population mean. (c) Construct a 99% confidence interval for the population mean. (d) Interpret the confidence interval you constructed in part (c).Solution
A.
The population mean we need here is he mean height of all corn plants in Iowa.
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B.
Note that
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 220
z(alpha/2) = critical z for the confidence interval = 1.959963985
s = sample standard deviation = 15
n = sample size = 100
Thus,
Lower bound = 217.060054
Upper bound = 222.939946
Thus, the confidence interval is
( 217.060054 , 222.939946 ) [answer]
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c.
Note that
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 220
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 15
n = sample size = 100
Thus,
Lower bound = 216.136256
Upper bound = 223.863744
Thus, the confidence interval is
( 216.136256 , 223.863744 ) [ANSWER]
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D.
We are 99% confident that the true mean is between 216.136 and 223.864. [ANSWER]
