The following random sample from a population whose values were normally distributed was collected. 10 8 11 11 The 95% confidence interval for μ is
A) 8.52 to 10.98
B) 7.75 to 12.25
C) 9.75 to 10.75
D) 8.00 to 10.00

Question

Quizplus · Accepted Answer

First, we need to calculate the sample mean (x̄) and sample standard deviation (s).

x̄ = (10+8+11+11)/4 = 10
s = √[(∑(x-x̄)^2)/(n-1)]
   = √[(2^2+(-2)^2+1^2+1^2)/3]
   = √6
   ≈ 2.45

Next, we need to find the t-value for a 95% confidence interval with n-1 degrees of freedom (df = 3 in this case). The t-value can be found using a t-table or calculator and is approximately 3.18.

Finally, we can calculate the confidence interval using the formula:
x̄ ± (t-value * (s/√n))
= 10 ± (3.18 * (2.45/√4))
= 10 ± 3.18 * 1.22
= 10 ± 3.89

So the 95% confidence interval for μ is 10 ± 3.89, which can be simplified to 7.11 to 12.89 or rounded to answer B, 7.75 to 12.25.

The Following Random Sample from a Population Whose Values Were