chapter 7: sampling distributions

Question 1

why do we make the sampling distribution of the sample mean’?

Answer 1

to see if we can use it do define the population mean

Question 2

what is the sampling distribution of the sample mean?

Answer 2

the probability distribution of the population of all the sample means that could be obtained from all possible samples of the same size

Question 3

what are the properties of he sampling distribution of the sample means?

Answer 3

often times, the distribution of all sample means looks like a normal shaped curve

the mean of all the possible population sample means is equal the the population mean

the standard deviation of all the possible sample means is less than the population standard deviation?

if the population is normally distributed, than all the possible samples will also be normal distributed

Question 4

why is the mean of all the possible population sample means an unbiased point estimate?

Answer 4

because it is equal to the population mean

Question 5

why is the standard deviation of all the possible sample means is less than the population standard deviation?

Answer 5

because each of the samples have less deviation and their values are actually closer to their mean

the extreme values per sample are gone, so there isn’t big differences

this make each standard deviation small

so the standard deviation of all the possible sample means is less than the population mean

Question 6

what is the formula to find the standard deviation of the population of all possible sample means?

Answer 6

standard deviation of chosen sample / (sqrt(sample population) )

the sample population must remain finite

population must be finite and be at least 20 times bigger than any sample size

Question 7

when calculating the standard deviation of all the possible sample means, what does it mean when n is bigger than 1

Answer 7

the standard deviation of all the possible sample means is less than the chosen sample mean

furthermore, as n increases, it decreases even more

the curve big¡come bigger upwards but tighter from side to side

Question 8

what is the formula for the variance of all possible sample means

Answer 8

(standard deviation of population)^(2/x))

another way (maybe) is ((standard deviation of population)^2) / n

Question 9

if the sampled population is not normally distributed, what are the formulas for the mean and standard deviation of all the possible sample means?

what is different or new?

Answer 9

they remain the same

what is new is the central limit theorem

Question 10

what is the central limit theorem?

Answer 10

is sample size n is large

then sampling distribution of all the possible means is normally distributed, even if population not normally distributed

the mean of all possible sample means as well as standard deviation of them have the same formulas

Question 11

how big must the sample size be if the population distribution is skewed?

Answer 11

the sample size has to be bigger the more skewed the population distribution is

in general, n = 30 means all sample distributions will be normally distributed

Question 12

the sampling distribution of a sample statistic

Answer 12

probability distribution of the population of all possible values of the sample statistic

Question 13

what makes the sample statistic an unbiased point parameter?

Answer 13

if the mean of the population of all possible values of the sample statistic equals the population parameter

Question 14

why do we call the sample mean a minimum variance of the population mean?

Answer 14

because we want it to be normally distributed and all clustered

we don’t want a big standard deviation or variance

both of them are gonna be close to the sample mean which is unbiased and very very very similar to the population mean

–> it is its point estimate

Question 15

what makes the sample variance an unbiased point estimate of the population variance?

Answer 15

if the sample population is infinite

Question 16

is there an easy way to calculate an unbiased point estimate of the population standard deviation?

Answer 16

nah boy

the sample standard deviation shouldn’t be considered an unbiased point estimate of the population standard deviation

Question 17

what is the finite population multiplier

give formula too

Answer 17

(N - n)/(N - 1)

you do the square root of that above

if N at least 20 times bigger than n, then the finite population multiplier is very close to 1

Question 18

what happens if N is not at least 20 times bigger than n

how does it affect the standard deviation of all possible sample means?

Answer 18

we have to use the finite population multiplier formula and add it to the original formula for the standard deviation of all possible sample means

Question 19

the sampling distribution of the sampling proportion

Answer 19

the population of all possible sample proportions

has a large n size

the mean of the sample proportion = the proportion of all the population

Question 20

how do you calculate the standard deviation of the sampling distribution of the sampling proportion

Answer 20

(p(1 - p) / n

square root of all dat

Question 21

this is the mean of the sampling distribution of the sampling proportion the same as “p”

Answer 21

because it is an unbiased point esiimate of “p”

Question 22

what happens to the standard deviation of the sampling distribution of the sampling proportion if n increases

Answer 22

its gonna decreases

cause values gonna be more clustered and normal distributed

Question 23

what makes a sample large enough to conclude that the distribution of the sampling proportion is approximately normal?

Answer 23

np > 5

qn > 5