Question

Question 2 4 pts For the following problem, use the given information to find the number of degrees of freedom, the critical values X1 and y, and the confidence interval estimate of o. You may assume that a simple random sample has been selected from a population with a normal distribution. Keep your numerical answers rounded to 3 decimal places. For a sample of heights in Men: 99% confidence; n = 125, = 7.10 cm, 1 - 1.9 m. DF= A B. C. = 99% CI estimate of o = Lower Limit: Upper Limit: HTML Editor BIVA-A- IE 3 11 XX, EE

Answer 1

Solution

Confidence Interval Formula for o is as follows: Square Root((n - 1)s2/x?a12)<o<Square Root((n - 1)52/X?1 - 12) where: (n - 1) = Degrees of Freedom, s2 = sample variance and a = 1 - Confidence Percentage First find degrees of freedom: Degrees of Freedom = n - 1 Degrees of Freedom = 125 - 1 Degrees of Freedom = 124 Calculate a a = 1 - confidence% a = 1 -0.99 a = 0.01 Find low end confidence interval value: diow end = a/2 dlow end = 0.0172 αιow -0.005 end Find low end x= value for 0.005 x20.005 = 168.3083 <--- -Value can be found on Excel using =CHIINV(0.005,124)

Calculate low end confidence interval total: Low End = Square Root((n - 1)sº/x?a/2) Low End = (124)(50.41)/168.3083) Low End = 16250.84/168.3083 Low End = 137.13922605124 Low End = 6.0942 Find high end confidence interval value: Anigh end = 1 -a/2 Ahigh end = 1 -0.01/2 Anigh end = 0.995 Find high end x value for 0.995 x20.995 = 87.1919 <--- Value can be found on Excel using =CHIINV(0.995,124) Calculate high end confidence interval total: High End = Square Root((n - 1)32/X?1 -a/2) High End = V(124)(50.41)/87.1919) High End = 16250.84/87.1919 High End = 171.690604287784 High End = 8.467 Now we have everything, display our interval answer: 6.0942 <O<8.467 <---- This is our 99% confidence interval