Confidence Interval

Question 1

How do you find the population mean within a stipulated confidence interval when population standard deviation (σ) is known?

Answer 1

μ = x̄ ± z_α/2 × (σ/√n)
x̄ = mean of sample
σ = population standard deviation
n = sample size
Z = z score
α = the probability that the interval will not contain the true population mean
μ = mean

Question 2

What can be said about the given confidence interval?

Answer 2

Confidence interval = 100(1-α)%,
where (1-α) is confidence level

Question 3

How do you find the population mean within a stipulated confidence interval when population standard deviation (σ) is not known?

Answer 3

μ = x̄ ± t_{(n-1, α/2)} • (s/√n)
x̄ = mean of sample
s = sample standard deviation
n = sample size
t = t score
α = the probability that the interval will not contain the true population mean
μ = mean
n -1 = degree of freedom

Question 4

What happens when population standard deviation is not given, and the ration of sample size to population size is high?

Answer 4

When n/N > 0.05,
s/√n becomes (s/n) • [ (N - n)/(N - 1)]^½
Thus,
μ = x̄ ± t_{(n-1, α/2)} × (s/n) • [ (N - n)/(N - 1)]^½
N = population size
n = sample size