MATH WEEK 7, 1, AND 2

Question 1

If random samples of size n are drawn from a population, then as n becomes larger, the sampling distribution of the mean approaches the normal distribution, regardless of the shape of the population distribution.

Answer 1

The Central Limit Theorem

Question 2

Applicable for a sufficiently large sample sizes n≥30.

Answer 2

The Central Limit Theorem

Question 3

The standard deviation of a sampling distribution, equals the standard deviation of the population divided by the square root of the sample size.

Answer 3

also known as Standard Error

Question 4

μ

Answer 4

Population mean

Question 5

σ

Answer 5

Population standard deviation

Question 6

µX̄ = µx.

Answer 6

The mean of the sampling distribution equals the mean of the population.

Question 7

µX̄

Answer 7

Sample mean

Question 8

σX̄

Answer 8

Sample standard deviation

Question 9

n

Answer 9

Sample size

Question 10

Although this concept was first developed by Abraham de Moivre in 1733, it wasn’t formally named until 1930, when noted Hungarian mathematician George Polya officially dubbed it the

Answer 10

Central Limit Theorem

Question 11

defined as a claim or guess.

Answer 11

Hypothesis

Question 12

a decision making process for evaluating claims about a population. It is a process of gathering evidences to either support or rebut a claim or guess. This claim or guess may or may not be true.

Answer 12

Hypothesis testing

Question 13

2 types of statistical hypothesis

Answer 13

Null Hypothesis
Alternative Hypothesis

Question 14

• A claim that denotes “absence” such as absence of difference, absence of relationship or equality to a certain value.
• It is a hypothesis of “no difference” and is denoted by H0.

Answer 14

Null Hypothesis

Question 15

• A claim that denotes “presence” such as presence of difference, presence of relationship or inequality to a certain value.
• It is a hypothesis of “no difference” and is denoted by Ha.

Answer 15

Alternative Hypothesis

Question 16

rejecting a true null hypothesis. It is denoted by alpha or (α).

Answer 16

TYPE I Error

Question 17

not rejecting a false null hypothesis. It is denoted by Beta or (β).

Answer 17

TYPE II Error

Question 18

the probability of committing a TYPE I error or alpha (α).

Answer 18

Level of Significance

Question 19

the range of values that indicates that there is a significant difference and that the null hypothesis should be rejected.

Answer 19

Rejection region

Question 20

A test concerning the mean of the normal population with known variance or standard deviation

Answer 20

z - test

Question 21

A large sample test concerning the mean of a population (using the central limit theorem)

Answer 21

z - test

Question 22

A small sample test concerning the mean of a population with unknown variance

Answer 22

t - test

Question 23

an assumption about a population which may or may not be true. It is also known as an inference about the population or parameter.

Answer 23

Statistical hypothesis

Question 24

Ho: parameter = specific value
Ha: parameter ≠ specific value

Answer 24

This is a two-tailed test (because of ≠); Non-directional

Question 25

Ho: parameter = specific value
Ha: parameter < specific value

Answer 25

This is a left- tailed test; directional

Question 26

Ho: parameter = specific value
Ha: parameter > specific value

Answer 26

this is a right- tailed test; directional

Question 27

the range of values of test value that indicates that there is a significant difference and that the null hypothesis should be rejected.

Answer 27

Rejection region or critical region

Question 28

is/are value/s that separate/s the rejection region from non-rejection regions

Answer 28

Critical value/s -