6. Estimation and Uncertainty

Question 1

R command to find z(α/2)

Answer 1

qnorm(1 - α/2, 0, 1)

This is the critical value when dealing with a standard normal distribution.

Question 2

Confidence interval for μ where σ^2 is known

Answer 2

x(bar) +- z(α/2) σ/sqrt(n)

Question 3

Confidence Interval for a Proportion

Answer 3

p(hat) +- z(α/2) sqrt( p(hat)(1 - p(hat)) / n)

Question 4

Bias

Answer 4

B(θ^, θ) = E(θ^) - θ

Question 5

Consistency (2 ways)

Answer 5

θ^n is consistent if for any ε>0,

lim(n -> infty) P( | θ^n - θ |

Question 6

Confidence Interval with t distribution

Answer 6

Use this when population variance is unknown and the sample is small:
x(bar) +- s/sqrt(n) t(n-1, α/2)
where s is sample s.d.

Question 7

R command to find critical value using chi-squared distribution

Answer 7

qchisq(α, v)

Question 8

R command to find critical value using t distribution

Answer 8

qt(1 - α/2, v)

Question 9

Confidence Interval using chi-squared distribution

Answer 9

Chi-squared dist is used for estimating variance.

sqrt(a)S