Inferential Statistics

Question 1

What is the kind of experiment conducted in Inferential Stats?

Answer 1

Drawing at random units from a population and measuring a characteristic of interest on them

Question 2

What are the properties of the arithmetic average from random variables?

Answer 2

1. It has mean (expected value) equal to the population mean μ
2. It has variance equal to the population variance divided my n (σ2/n)
3. Based on the Central Limit Theorem, for a large sample size n, it has distribution that can be approximated by the normal (or Gaussian) distribution

Question 3

What are the properties of the sample proportion ^p?

Answer 3

1. It has mean equal to the population mean p
2. It has variance equal to the population variance divided my n (^p(1-^p)/n)
3. Has distribution that can be approximated for large n by a normal distribution with mean p and variance (^p(1-^p)/n)

Question 4

Is the sample mean biased or unbiased?

Answer 4

Unbiased

Question 5

As n increase does the sample variance increases or decreases?

Answer 5

Decreases

Question 6

Is the sample mean consistent or unconsistent?

Answer 6

Consistent

Question 7

What is the estimated population variance?

Answer 7

s^2/n

Question 8

How is the estimated sd calculated?

Answer 8

S/sqrt n

Question 9

What is the sample proportion estimator?

Answer 9

p(1-p)/n

Question 10

What is the sample proportion standard error?

Answer 10

sqrt(p(1-p)/n)

Question 11

What is a confidence interval?

Answer 11

Provides an approximation of the parameter and at the same time a probabilistic assessment of the approximation error that we make

Question 12

The ……(greater/lower) the standard error, the ……(greater/lower) the accuracy of the estimator

Answer 12

lower, greater

Question 13

Normal pop with known variance (r command)

Answer 13

qt(1-a/2,%)

Question 14

Normal pop with known variance “formula”

Answer 14

(X-+z(a/2,a-1)*(σ/sqrt(n))

Question 15

The higher the population variance, the …… the standard error

Answer 15

higher

SE= σ^2/n

Question 16

Is za/2 higher for a 90% interval, compared to a 99% one?

Answer 16

No

There is a trade off between the length of the confidence interval and confidence level

Question 17

Normal pop with unknown μ (r)

Answer 17

qnorm(1-a/2)

Question 18

R command for CI of prop

Answer 18

qnorm(1-a/2)

Question 19

CI command for R data

Answer 19

t.test(variable name, confidence level)