Respuesta :
Answer: Â a) (176.76,172.24), b) 0.976.
Step-by-step explanation:
Since we have given that
Mean height  = 174.5 cm
Standard deviation = 6.9 cm
n = 50
we need to find the 98% confidence interval.
So, z = 2.326
(a) Construct a 98% confidence interval for the mean height of all college students.
[tex]x\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=(174.5\pm 2.326\times \dfrac{6.9}{\sqrt{50}})\\\\=(174.5+2.26,174.5-2.26)\\\\=(176.76,172.24)[/tex]
(b) What can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5 centime- ters?
Error would be
[tex]\dfrac{\sigma}{\sqrt{n}}\\\\=\dfrac{6.9}{\sqrt{50}}\\\\=0.976[/tex]
Hence, a) (176.76,172.24), b) 0.976.
