Answer:
Step-by-step explanation:
Given Parameters
Mean,
= 180
total samples, n = 20
Standard dev,
= 30
= 1 - 0.95 = 0.05 at 95% confidence level
Df = n - 1 = 20 - 1 = 19
Critical Value,
, is given by
![t_{c}=t_{\alpha, df} = t_{0.05,19} = 1.729](https://tex.z-dn.net/?f=t_%7Bc%7D%3Dt_%7B%5Calpha%2C%20df%7D%20%3D%20t_%7B0.05%2C19%7D%20%3D%201.729)
a).
Confidence Interval,
, is given by the formula
![\mu = x +/- t_c \times \frac{s}{\sqrt{n} }](https://tex.z-dn.net/?f=%5Cmu%20%3D%20x%20%2B%2F-%20t_c%20%5Ctimes%20%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%20%7D)
![\mu = 180 +/- 1.729 \times \frac{30}{\sqrt{20} }](https://tex.z-dn.net/?f=%5Cmu%20%3D%20180%20%2B%2F-%201.729%20%5Ctimes%20%5Cfrac%7B30%7D%7B%5Csqrt%7B20%7D%20%7D)
![\mu = 180 +/-11.5985](https://tex.z-dn.net/?f=%5Cmu%20%3D%20180%20%2B%2F-11.5985)
b).
Critical Value,
, is given by
![t_{c}=t_{\alpha/2, df} = t_{0.05/2,19} = 2.093](https://tex.z-dn.net/?f=t_%7Bc%7D%3Dt_%7B%5Calpha%2F2%2C%20df%7D%20%3D%20t_%7B0.05%2F2%2C19%7D%20%3D%202.093)
Confidence Interval,
, is given by
![\mu = x +/- t_c \times \frac{s}{\sqrt{n} }](https://tex.z-dn.net/?f=%5Cmu%20%3D%20x%20%2B%2F-%20t_c%20%5Ctimes%20%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%20%7D)
![\mu = 180 +/- 2.093 \times \frac{30}{\sqrt{20} }](https://tex.z-dn.net/?f=%5Cmu%20%3D%20180%20%2B%2F-%202.093%20%5Ctimes%20%5Cfrac%7B30%7D%7B%5Csqrt%7B20%7D%20%7D)
= 180 +/- 14.0403
= 165.9597 <
< 194.0403