it 07 minutes retpectively veur thandard deviation to th.pdf

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The document discusses how sample size affects the center and variability of sampling distributions. It asks the reader to calculate and compare the centers and standard deviations of three samples with different sizes. Larger sample sizes result in distributions with larger centers and smaller standard deviations. The largest sample size of n=160 would be most likely to produce a value of x close to the population mean, due to its smaller standard deviation.

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it =0.7 minutes, retpectively. veur thandard deviation to three decimat places-) (b) Repeat part (a)
for iample of size of n=20. (Pesind your standard deviathan to three decimal places.) Bavest Eart
(a) again for a uncte of ure of A=160. (fiosha your standard deviatoon to theee docimai pacesi)
How de the cehters and variabisities de the thire x samplaig distributions compare to one another?
The larper the sample sice, the larger the center and the maller the standard deviation of the x
distrikution. The larger the sample sue, the larger the center and the standard deviatien of the x
distribjes. The three centeis are all the same, and the arper the sample me, the semalier the
standard derviation of the x distribution. The Iaroer the sample cae, the amaler the oenter and the
standard devation of the x distrisution. The tfres cenctets are al the same, and the larger the
sample size, the larger the standard deviation of the x astrbution. Which sprole alee woud be most
ikedy to reault in an x value iloce to , and whe? Since the sainging distribstos of when n is 100B a
has the standard deviation, this sample size is most likely to resus in a value of x ewere ras in

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Assignment #9 First, we recall some definitions that will be helpful in answering questions 1-3 A population parameter is a single value that describes a population characteristic (such as center, spread, location etc.) EXAMPLES: · The proportion p of adults in the United States who worry about money · The mean lifetime m of a certain brand of computer hard disks · The lower quartile 1 q of a population of incomes · The standard deviation s of the nicotine content per cigarette produced by a certain manufacture. In real life, population parameters are usually unknown. An important objective of statistical inference is to use information obtained from random sample or samples (depending on the design of the study) to estimate parameters and to test claims made about them. A statistic is a number computed form the sample data only. The resulting sample value must be independent of the population parameters. Statistics are used as numerical estimates of population parameters. Example: A random sample of 1500 national adults shows that 33% of Americans worry about money. The margin of error is +/- 3 percentage points. Statistics have variation. Different random samples of size n from the same population will usually yield different values of the same statistic. This is called sampling variability. The sampling distribution of a statistic is the distribution of the values taken by the statistic over all possible random samples of the same size from a given population. What do we look for in a sampling distrinution? Bias: A statistic is unbiased if its sampling distribution has a mean that is equal to the true value of the parameter being estimated by that statistic. Variability: How much variation is there in the sampling distribution? The goal of this assignment is to simulate the sampling distribution of some statistics. Question 1: An urn contains 50 beads. The beads are identical in shape and have one of two colors: blue and orange. We would like to estimate the proportion p of blue beads. We select without replacement a sample of 10 beads. The relevant statistics is the sample proportion p ˆ of blue beads (i.e., the number of blue beads in the sample divided by 10. For the purpose of the simulation exercise, we will assume that the box contains exactly 15 blue beads or, equivalently, the proportion of blue beads is 30 . 0 = p . i) Select 100 samples of size 10 from the box. ii) Compute the sample proportion p ˆ of blue beads for each of the 100 samples found in (i). iii) Make a histogram of the values of p ˆ found in (ii) (that is the approximate sampling distribution of p ˆ .) iv) Find the summary statistics of the 100 values of p ˆ . v) Base yourself on the histogram and the summary statistics to describe the approximate sampling distribution of p ˆ . vi) Is p ˆ an unbiased estimator of p ? Hint: Evaluate the difference between 30 . 0 = p and the mean value. ...

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