please show all work thank you Problem 4 Corn Plants 12 pts

please show all work. thank you!

Problem 4. (Corn Plants) [12 pts] An agronomist measured the heights of loo corn plants in Iowa. Within his sample, he found that the mean height was 220 cm and the standard deviation was 15 cm. State in words the population mean of this problem. Construct a 95% confidence interval for the population mean. Construct a 99% confidence interval for the population mean. Interpret the confidence interval you constructed in part (c).

Solution

a) Population mean of this problem = 220cm

b) Mean = 220cm
z for 95% confidence interval = 1.96
Standard Error = z* SD / sqrt(n)
= 1.96 * 15 / sqrt(100) = 2.94
95% confidence interval = ( 220 - 2.94 , 220 + 2.94)
= (217.06,222.94) Answer

c) Mean = 220cm
z for 99% confidence interval = 2.575
Standard Error = z* SD / sqrt(n)
= 2.575 * 15 / sqrt(100) = 3.8625
99% confidence interval = ( 220 - 3.8625 , 220 + 3.8625)
= (216.1375,223.8625) Answer

d)
We are 99% sure that the interval contains the population mean.