Question

(a) Find the sample mean.
​(b) Find the sample standard deviation.
​(Round to one decimal place as​ needed.)
​(c) Construct a 95​% confidence interval for the population mean mu.
A 95​% confidence interval for the population mean is ​
​(Round to one decimal place as​ needed.)

4450.53 4596.55 4366.15 4455.88 4151.86 3727.78 4283.99 4527.68 4407.21 3946.58 4023.44 4221.79

Answer 1

a)

Sample Mean = x̄ = Σxᵢ / n = 51159.44 / 12 = 4263.28

Sample Variance = s² = Σ(x_i - x̄)²/(n - 1) = 743578.76/11 = 67598.06

b)

Sample Standard Deviation = s = √ Sample Variance = √67598.06 = 259.9

c)

Step 1: Find α/2
Level of Confidence = 95%
α = 100% - (Level of Confidence) = 5%
α/2 = 2.5% = 0.025


Step 2: Find t_α/2
Calculate t_α/2 by using t-distribution with degrees of freedom (DF) as n - 1 = 12 - 1 = 11 and α/2 = 0.025 as right-tailed area and left-tailed area.

Step 3: Calculate Confidence Interval

t_α/2 = 2.200985

Lower Bound = x̄ - t_α/2•(s/√n) = 4263.28 - (2.200985)(259.99/√12) = 4098.1

Upper Bound = x̄ + t_α/2•(s/√n) = 4263.28 + (2.200985)(259.99/√12) = 4428.5

Confidence Interval = (4098.1, 4428.5)