Term
| What two purposes do Probability distributions serve? |
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Definition
(1) They allow us to answer probability questions about sample statistics
(2) They provide necessary theory for making statistical inference procedures valid. |
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Term
| A sampling distribution is __ |
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Definition
| The distribution of all possible values that can be assumed by some statistic, computed from samples of the same size randomly drawn from the same population |
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Term
| How do you compute a sampling distribution for a discrete, finite population? |
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Definition
1. randomly draw all possible samples of size n
2. compute statistic of interest for each sample
3. list in 1 column the different distinct observed values of the stat and in another column list the corresponding frequency of occurrence of each distinct observed value of the statistic |
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Term
| How do you compute a sampling distribution for an infinite population? |
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Definition
| You can APPROXIMATE one by taking a large number of samples |
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Term
| What are the three big things to know about a sampling distribution? |
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Definition
mean
variance
function form (what it looks like graphed) |
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Term
| If you have 5 cows and take a random sample of 2, how many possible combinations can you get? |
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Definition
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Term
| What is the formula for the sample population mean? |
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Definition
[image]
u=sum of sample means/Number in population^number of times you sample |
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Term
What is the formula for variance of the sampling distribution?
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Definition
[image]
Sum of the (sample mean-population mean)/Number in population^number of times sampled |
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Term
Is the mean and variance a biased or unbiased estimator?
Why? |
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Definition
Mean is unbiased
Variance is biased
The mean of the population is the same as the mean of the sampling distribution.
The variance of the population is not the same as the variance of the sampling distribution.
[image][image] |
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Term
| Variance of the sampling distribution is equal to: |
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Definition
lvariance of the sampling distribution is equal to the population variance/size of the sample |
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Term
| Formula for standard error of the mean (SEM) |
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Definition
[image]
standard deviation/ square root of number of samples taken |
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Term
l.smfd;skf;lmibeoue[potre;lbIn a normally distributed population, the distribution of the sample mean will have these following properties: |
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Definition
l(1) The distribution of x-bar will be normal.
l(2) The mean, u , of the distribution of x-bar will be equal to the mean of the population from which the samples were drawn.
l(3) The variance of the distribution of x-bar will be equal to the variance of the population divided by the sample size. |
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Term
lWhen sampling from a non-normally distributed population, we refer to an important mathematical theorem known as the _____ |
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Definition
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Term
| What is the central limit theorem? |
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Definition
| a population of any non-normal functional form will be approximately normally distributed when the sample size is large. |
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Term
How do you know you can use a normal distribution?
(3 possibilities) |
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Definition
lwkljsdflskajdf;laskjfdlkjsd(
1) When sampling from a normally distributed population
llskjdflskadflak;sjdflmvwemf(
2) When sampling from a non-normally distributed population and our sample size is great
lslakdjf;weijgb'wqlmdd'Q[WPKR3
(3) When sampling from a population whose functional form is unknown to us as long as our sample size is great |
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Term
| When is your sample size large enough according to the central limit theorem to use a normal distribution? |
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Definition
| Depends on how weird your distribution is, but generally n=30 is large enough. |
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Term
Know:
(1) a single sample mean, (2) the difference between 2 sample means, (3) a sample proportion, and (4) the difference between 2 sample proportions. |
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Definition
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Term
| You look at the difference between two sample means when...? |
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Definition
| You want to know if the two populations are different, or what the magnitude of the difference is. |
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Term
How would you solve this:
If there is no difference between the 2 populations, with respect to their true blood glucose concentrations, what is the Pr of observing this large or larger difference between sample means? |
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Definition
we need to know the nature of the sampling distribution of the relevant statistic, the difference between 2 sample means
Create a relative frequency histogram based on the differences between the two sample means by determining all the possible means for finite population 1 and same for 2 |
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Term
| What's the z score formula for the distribution of the difference between two sample means? |
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Definition
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Term
Sometimes we're interested in a sampling distribution of a statistic such as a sample proportion that results from count of frequency data
What is an example of this? |
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Definition
lIn a certain population 0.08 flowers are red. If we designate a population proportion, p, we can say that in this example p=0.08. If we randomly select 150 flowers, what is the Pr that the proportion of red flowers will be as great as 0.15? |
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Term
| The frequency histogram of the differenc of two sample means would have a mean of___ and a variance equal to ____ |
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Definition
mean= u1-u2
variance= var/number of samples for population 1 + var/number of samples for population 2 |
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Term
| How do you construct a sampling distribution of a sample proportion? |
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Definition
Similar to a distribution for the difference between two means.
1. take all possible samples from a finite population and compute the sample proportion for each sample.
2. prepare a frequency distribution of sample proportion (p hat) by listing different distinct values of phat with their frequencies of occurrence. |
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Term
| by the virtue of _____ the distribution of sample proportions is approximately normally distributed when sample size is ____ |
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Definition
central limit theorem
large |
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Term
| mean of the sample proportion distribution is ______ and is equal to _____ |
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Definition
the average of all possible sample proportions
= to the true population proportion (p) |
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Term
| formula for variance of sample proportion distribution |
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Definition
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Term
| how to convert to z score for sample proportion distribution: |
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Definition
| z= phat-p /square root of variance |
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Term
| How large does the sample size have to be for the use of the normal approximation to be valid for a sample proportion distribution? |
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Definition
| n(p) and n(q) must be greater than 5 |
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Term
distribution of the difference btwn 2 sample proportions
mean and variance formulas |
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Definition
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Term
| When can you use CLT for distribution between 2 sample proportions? |
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Definition
| When n1p1, n2p2, n1(1-p1), and n2(1-p2) are large, > 5 |
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Term
| How do you convert to z score for distribution of 2 sample proportions? |
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Definition
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