Question

While answering the questions on this exam assume that you have a SAMPLE of size 16 selected out of a large population (i.e., N+) where X represents the weight of adult males measured in pounds (i.c., pounds = #): n=16 X= 180# S = 6400#2 Which implies that, v=df-n-1 = 16-1 = 15 Sx = S = 640042 = 80# Sy = S = so = 20$ 1. Construct the 90 percent confidence interval for the MEAN of X. (= 90 a=1-c..10 ala-,05 vin-1 = 16-1 = If the true value of the MEAN of X is equal to 222 pounds which lies above the upper boundary and outside of the confidence interval have you committed a statistical error in the previous question? Explain! 3. In what type of units is the value of the upper boundary of the confidence interval measured? Be specific!

Answer 1

1. The 90% confidence interval for the mean is:

$\small \bar{X}\pm t_{0.5,15}*s_{\bar{X}}=180\pm 1.753*20=(144.94,215.06)$

2. Here the true mean is 222 pounds, which lies above the upper boundary. Then, we might have made a Typee II error.

3. Here X is the weight in pounds. Thus the units of the upper confidence interval are pounds.