2 Normal Distribution & Inferences

Question 1

What are the properties of a normal distribution?

Answer 1

• bell shaped
• symmetrical
• mean, median and mode equal

Question 2

What does the central limit theorem state?

Answer 2

Anything you can average over a large enough number will give you a normal distribution curve

Question 3

What 2 parameters determine the shape of a normal curve?

Answer 3

Mean- line of symmetry
SD- how spread out the data is

Question 4

What is the empirical rule?

Answer 4

In a normal distribution curve:
68% of data within 1SD
95% of data within 2SD
99.7% of data within 3SD

Question 5

If we measure student heights and we know height is normally distributed do we still have to check normality of the data?

Answer 5

Yes
Sample and population

Question 6

What is a population and what is a sample?

Answer 6

Population: group of all items of interest
Sample: set of data drawn from population

Question 7

What is a parameter and what is a statistic?

Answer 7

Parameter is a descriptive measure of a population
Statistic is a descriptive measure of a sample

Question 8

What is inferential statistics?

Answer 8

Draw conclusions or inferences about characteristics of populations based on data from a sample

Question 9

What is a statistical inference?

Answer 9

An estimate, prediction or decision about a population based on a sample

Question 10

What is sampling variation

Answer 10

How sample statistics can vary from sample to sample due to random chance

Question 11

What is standard error?

Answer 11

Measure of sampling variability

Question 12

What factors reduce standard error/sampling variability?

Answer 12

Increased sample size
Lower variability of outcome

Question 13

How do we calculate Standard error?

Answer 13

Standard deviation of sample statistic

Question 14

Sampling variability

Answer 14

Sampling variability = standard error = SD of sample statistic

Decrease w inc sample size
Increase w inc variability if outcome

Question 15

How do we calculate confidence intervals?

Answer 15

(Sample statistic)+- (confidence level)xSE

If we want to be 95% confident = 1.96

Question 16

If the 95% confidence interval for the mean is (29.6, 46.9) what does is mean??

Answer 16

There is a 95% probability that the true population mean lies within 29.6 and 46.9

Question 17

How can we check if our data is normally distributed?

Answer 17

Histogram- is it bell shaped?
Descriptive summary- are mean, median and mode similar?
Does 68% of data like within 1 SD of mean? 95% within 2 SDs?
Q-Q plot - linear
Normality test - sig>0.05

Question 18

What are the normality test we can run?
Why do we have to be cautious

Answer 18

Kolmogorov-Smirnov - normal probability plot, if normal it will be linear
Highly influenced by sample size

Question 19

Why do we have confidence intervals and significance levels?

Answer 19

Conclusions and estimates based on sample statistics need measures of reliability

Question 20

What does confidence level measure?

Answer 20

Proportion of times that an estimating procedure will be correct

Question 21

What does the significance level measure?

Answer 21

How frequently the conclusion will be wrong in the long run. 5% sig level= conclusion will be wrong 5% of the time in the long run

Question 22

How do we illustrate significance and confidence level

Answer 22

Alpha = significance
Confidence = 1-alpha

Therefore significance + confidence level = 1

Question 23

If the sample increases, what would you expect would happen to the confidence interval?

Answer 23

Sample size increases so standard error reduces so confidence interval becomes narrower

Question 24

How do we calculate the sample proportion for categorical data like success/fail?

Answer 24

no. successes in sample/total count in sample = p hat = “sample proportion” = mean of sample proportion

Question 25

As the sample size increases, the sample proportion distribution becomes ?

Answer 25

Normal (approximately)

Question 26

If we repeat samples again and again we will eventually get a normal distribution of the sample mean. What are the conditions for this to take place?

Answer 26

Random sampling - no selection bias
Sample is large enough (>10) & n(p) and n(1-p) >5 (p is mean)

Question 27

What are the 2 methods of assessing normality?

Answer 27

Q-Q plot - straight line
Kolmogorov Smironov test (sig>0.05)

Question 28

What is the central limit theorem?

Answer 28

For quantitative data, the sample size is large enough (n>30), distribution of the sample mean (if survey repeated 10000 times), would be Normal distribution.

For categorical data, the sample proportion distribution would be normal (if survey repeated 10000s times) but only following certain conditions.

Question 29

What are the conditions necessary for central limit theorem to be valid for categorical data (sample proportion distribution to be normal)

Answer 29

Sample size must be large enough
np>=5 and n(1-p)>=5
Randomised selection of sample (no bias)

Question 30

How do we calculate the CI for 95% confidence level?

Answer 30

CI = sample statistic +- (1.96 x SE)