Sampling, Standard Error of the Mean, Confidence Intervals

Question 1

All cases (usually people) that you are interested in, is known as ______.

Answer 1

population

Question 2

Ideally you want to have the whole population’s results however this isn’t realistic, so what do studies do instead?

Answer 2

They study samples.

Question 3

What is a sample?

Answer 3

A subset of the population.

Question 4

What do you need to do in order to generalise the results of your study to the whole population?

Answer 4

Look at how representative your sample is of the population.

Question 5

Using the class as the population- the class mean on the class  test was 74.87.
What will give us different means?

Answer 5

We take samples of this population e.g. 5 students and find the mean of their scores, and plot this on the graph.

Question 6

Why do different samples have different means?

Answer 6

Due to random error :)

Question 7

What does random error reflect?

Answer 7

Random error simply reflects that we aren’t all perfect representations of the population- people are different!

Question 8

What happens if you keep taking the means from lots of different samples of the class/population, and plot it?

Answer 8

We end up with a normal distribution- peaking at the population mean :)
Each dot on the graph represents a different sample.

Question 9

Sample means closer to the population mean will occur ____ frequently than sample means which are further away from the population mean.

Answer 9

MORE

Question 10

Although the sample means might differ- where do the majority congregate?

Answer 10

Around the population mean :)

Question 11

How do you get a better estimate of your population?

Answer 11

Have a big sample size :)

Question 12

As sample size increases….

Answer 12

standard error decreases.

Question 13

Why do we calculate standard error?

Answer 13

To tell if our sample is a good estimate of the population mean.

Question 14

The _____ tells us about the variability in sample means.

Answer 14

standard error.

Question 15

What is standard error similar to?

Answer 15

Standard deviation! But instead of variation in scores, it’s variation in sample means :)

Question 16

What does a small standard error suggest?

Answer 16

That you have a relatively accurate estimate of the population mean.

Question 17

What does a large standard error suggest?

Answer 17

That you have a less accurate estimate of the population mean :(

Question 18

How do you calculate standard error?

Answer 18

SD/ square root of N

N= number of scores

Question 19

Calculate the standard error:
N= 5
SD= 11.71
Mean= 72.60

Answer 19

11.71/ square root of 5

SE= 5.23

Question 20

If the standard error is 5.23 and the mean is 72.60 what does this tell us about the means of the samples?

Answer 20

It tells us that 68% of the means of samples of 5 students will land between
(72.6+/- 5.23) 67.37 and 77.83.

Question 21

What percent of sample means will fall 1 SD below and 1 SD above the population mean?

Answer 21

34.13 + 34.13 = 68.26% 0r normally just say 68%.

Question 22

Saying 68% of the sample will fall within a range isn’t v helpful, this is why we use ________

Answer 22

confidence intervals!

Question 23

_______ allows us to express a range of scores around the mean with greater confidence

Answer 23

Confidence Intervals

Question 24

A larger sample size will mean that the CI becomes ______.

Answer 24

Smaller- because you are confident about the true mean lying within a smaller range of values.

Question 25

What is the standard CI that is used?

Answer 25

95% CI :)

Question 26

95% of all scores fall within ______ standard deviations above and below the mean.

Answer 26

1.96

Question 27

(like SD)95% of sampling means fall within +/- 1.96 ______ _______.

Answer 27

standard errors.

Question 28

How do you calculate the 95% CI?

Answer 28

Multiple the standard error by 1.96.

Then add that value to the mean to find the upper limit and subtract it from the mean to find the lower limit.

Question 29

Calculate the 95% CI:
mean = 72.6
SE= 5.23

Answer 29

5. 23 x 1.96 = 10.25
6. 6 + 10.25 = 82.85
7. 6 - 10.25 = 62.35

Question 30

If the confidence intervals (for samples) are 62.35 and 82.25, what does this mean?

Answer 30

95% of the mean samples will have a mean between 62.35 and 82.25.

Question 31

The _____ the sample size the smaller the CI.

Answer 31

Bigger.

Question 32

How can CI’s be displayed?

Answer 32

on graphs- like we used to draw for bio at school!

Question 33

What tells you about variability in sample means?

Answer 33

Standard error

CI (more informative)

Question 34

What is more informative than Standard error?

Answer 34

Confidence Intervals