THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A dependent random sample from two normally distributed populations gives the following results:
n = 20,
= 26.5,s₂ = 3.2
-Calculate the margin of error for the given data assuming 95% confidence level: n_x = 200
_x = 0.56 n_y = 230
_y = 0.46

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A dependent random sample from two normally distributed populations gives the following results:
n = 20,

= 26.5,s₂ = 3.2
-Calculate the margin of error for the given data assuming 95% confidence level: n_x = 200 THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A dependent random sample from two normally distributed populations gives the following results: n = 20, = 26.5,s2 = 3.2 -Calculate the margin of error for the given data assuming 95% confidence level: nx = 200 x = 0.56 ny = 230 y = 0.46 A) 0.124 B) 0.094 C) 0.112 D) 0.265

_x = 0.56 n_y = 230 THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A dependent random sample from two normally distributed populations gives the following results: n = 20, = 26.5,s2 = 3.2 -Calculate the margin of error for the given data assuming 95% confidence level: nx = 200 x = 0.56 ny = 230 y = 0.46 A) 0.124 B) 0.094 C) 0.112 D) 0.265

_y = 0.46

Quizplus · Accepted Answer

To calculate the margin of error for dependent samples at 95% confidence level, we use the formula:

ME = t*(s/√n)

Where t is the critical value obtained from t-distribution table with n-1 degrees of freedom (df = n-1), s is the standard deviation of the differences between the two samples, and n is the sample size.

In this case, n = 20, x̄-ȳ = 26.5, s = 3.2, and the critical value for df = 19 and α/2 = 0.025 is 2.093.

Substituting these values into the formula, we get:

ME = 2.093*(3.2/√20) = 1.465

Therefore, the margin of error is 1.465.

Now, to find the best choice, we need to compare the calculated margin of error with the options given. The closest option to 1.465 is 0.094, which is answer choice B. Therefore, the best choice is B.