Please show steps and formulas. Thanks! Two independent sampling stations (upstr
ID: 3154982 • Letter: P
Question
Please show steps and formulas. Thanks!
Two independent sampling stations (upstream and downstream) were chosen to study the effectiveness of a species diversity index in indicating aquatic degradation due to acid mine drainage. For 12 monthly samples collected at the downstream station, the species diversity index had a mean value x_1 = 3.11 and a std. dev. s_1 = 0.771, while 10 monthly samples collected at the upstream station had x_2 = 2.04 and s_2 = 0.448. Find a 90% CI for the difference between the population means for the two locations, assuming that the populations are approx, normally distributed with equal variances.Explanation / Answer
Calculating the means of each group,
X1 = 3.11
X2 = 2.04
Calculating the standard deviations of each group,
s1 = 0.771
s2 = 0.448
Thus, the pooled standard deviation is given by
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]
As n1 = 12 , n2 = 10
Then
S = 0.645956152
Thus, the standard error of the difference is
Sd = S sqrt (1/n1 + 1/n2) = 0.2765819
For the 0.9 confidence level, then
alpha/2 = (1 - confidence level)/2 = 0.05
t(alpha/2) = 1.724718243
lower bound = [X1 - X2] - t(alpha/2) * Sd = 0.357572237
upper bound = [X1 - X2] + t(alpha/2) * Sd = 1.782427763
Thus, the confidence interval for u1 - u2 is
( 0.357572237 , 1.782427763 ) [ANSWER]
*****************************************************
Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!