samples and populations 2

Question 1

why do we use a sample to estimate the population

Answer 1

it is impossible to collect data from whole pop and need to generalise to whole pop

Question 2

what are inferential stats

Answer 2

infer from sample to pop

measure stats of sample and infer parameters of pop

Question 3

what happens when we have a sample of data

Answer 3

can calculate stats for sample that know to be true for sample as KNOW sample stats of MEAN and SD

Question 4

what are population parameters

Answer 4

MEAN and SD are parameters; not generally known but use sample stats to ESTIMATE parameters for pop

Question 5

why do we apply sampling theory

Answer 5

need to see if sample mean is good est of pop mean and see what sample size to use

Question 6

what is sample mean

Answer 6

unbiased estimator of pop mean that will rarely be same as pop mean due to error; still, equal to pop mean

Question 7

what is the sampling distrib and what does it tell us

Answer 7

sampling a variety of samples from the wider population and compute various statistics for each sample; is the distribution of these statistics

tells us degree to which samples from larger pop may vary and what valeus may expect to obtain from particular stat under set of predefined conditions

Question 8

what is the sampling distrib of the mean

Answer 8

distrib of all poss sample means

Question 9

what is the first part of central limit theory

Answer 9

mean of all possible sample means will be equal to the population mean.

Question 10

what does central limit theory tell us

Answer 10

when have sampling distrib of mean, tells us abt properties of sample in relation to pop

Question 11

outline CLT part 1

Answer 11

have a population of scores with a mean of mu and a standard deviation of sigma, then the sampling distribution of the mean will have a mean of mu

Question 12

how do you calculate the spread of sample means

Answer 12

calculate sample SD of sample means

Question 13

what is the SD of sampling error of sampling distribution of the mean called

Answer 13

standard error SE of mean

Question 14

what is the SE a measure of

Answer 14

expected variability for a particular statistic among samples; gets smaller as sample size increases ; thus tells us how far sample means fall from pop mean

Question 15

how does SE differ from SD

Answer 15

SD is measure of single score differing from mean; SE is measure of amount sample mean differs from pop mean

Question 16

what is CLT part2

Answer 16

The sampling distribution of the mean will have a standard deviation of o√N

SE dependent on sample size; sample distribution will be different for each sample size

Question 17

what does central limit theorem tell us

Answer 17

how to calculate the standard deviation of the sampling distribution of the mean, without having to work out all possible sample means.

Question 18

what does it mean if the SD is large and what does this tell us about our mean as an estimate of pop mean

Answer 18

all poss sample means are spread out around pop mean so sample has potential to fall long way from pop mean
gives measure of how much mean likely to be wrong as estimate of pop mean

Question 19

what does N become when looking at distribution of sample means

Answer 19

sample size not number os samples

Question 20

why is one sample abetter estimate of pop mean

Answer 20

because there’s less spread in possible sample means that could get

Question 21

what do larger samples produce in terms of standard errors

Answer 21

smaller sample errors

Question 22

what does it mean if the sample means is a narrow distribution

Answer 22

sample means will fall close to population mean

Question 23

what does it mean if the sample means is a wide distribution

Answer 23

sample mean has chance of falling far from population mean

Question 24

what is central limit theorem part 3

Answer 24

If the population of scores is normally distributed, the sampling distribution of the mean will be normally distributed.
if not normally distributed, The sampling distribution of the mean will approach the normal distribution as the sample size (N) increases, regardless of the shape of the original population distribution.

Question 25

how does central limit theorem sum up sampling distribution of the mean

Answer 25

1. First it specifies that the distribution of sample means will have a mean equal to the value of population mean, mu.
2. Second the distribution of means will have a standard deviation equal to the standard error, σ/√N.
3. Third, as samples gets larger (large is usually defined as 30 or more, bit in some cases it will be much more) the distribution of sample means will become normal.