Question

a. Use the​ one-mean t-interval procedure with the sample​ mean, sample​ size, sample standard​ deviation, and confidence level given below to find a confidence interval for the mean of the population from which the sample was drawn.

b. Obtain the margin of error by taking half the length of the confidence interval. c. Obtain the margin of error by using the formula t Subscript alpha divided by 2 Baseline times StartFraction s Over StartRoot n EndRoot EndFraction .

x=30 n=25 s=3 confidence level= 99%

Answer 1

Solution:- Given that x = 30, n = 25, s = 3, confidence level = 99%

n = 25, df = n-1 = 24, t = 2.7969

a. 99% confidence interval about μ is 28.3219 to 31.6781
=> X +/- t*s/sqrt(n) = 30 +/- [ 2.7969*3/sqrt(25) ] = (28.3219,31.6781)

b. the margin of error found by taking half the length of the confidence interval is 1.7296

When margin of error taking half of length of confidence interval is : (31.6781-28.3219)/2 = 1.7296

c. Margin of error is t*s/sqrt(n)

2.7969*3/sqrt(25) = 1.6781