Question

Please give a careful but brief answer to each of the following questions. (a) What is a population? A population is the complete set of measurements from every individual of interest. A population is a subset of the complete set of measurements from every individual of interest. A population is a numerical descriptive measure of the complete set of measurements from every individual of interest. A population is a numerical descriptive measure of a subset of the complete set of measurements from every individual of interest. Incorrect: Your answer is incorrect. . . How do you get a simple random sample? A simple random sample is accomplished by dividing the entire population into pre-existing segments. Make a random selection of segments. Include every member of each selected segment in the sample. A simple random sample is accomplished by numbering all members of the population sequentially. Then, from a starting point selected at random, include every kth member of the population in the sample. A simple random sample is accomplished by dividing the entire population into distinct subgroups based on a specific characteristic such as age, income, education level, and so on. All members of a subgroup share the specific characteristic. Draw random samples from each subgroup. A simple random sample is accomplished by assigning numbers to members of the population and then using a table, calculator, or computer to select random numbers from the numbers assigned to the population members. Create the sample by using population members with numbers corresponding to those randomly selected. A simple random sample is accomplished by using data from population members that are readily available. Incorrect: Your answer is incorrect. . . Give examples. This answer has not been graded yet. . (b) What is a sample statistic? A sample statistic is the complete set of measurements from every individual of interest. A sample statistic is a subset of the complete set of measurements from every individual of interest. A sample statistic is a numerical descriptive measure of the complete set of measurements from every individual of interest. A sample statistic is a numerical descriptive measure of a subset of the complete set of measurements from every individual of interest. What is a sampling distribution? A sampling distribution is a probability distribution of a ---Select--- population population parameter sample sample statistic based on all possible ---Select--- populations simple random samples of ---Select--- the same size different sizes from ---Select--- the same population different populations . Give examples. This answer has not been graded yet. . (c) Give a careful and complete statement of the central limit theorem. Given a probability distribution of x values where n = sample size, μ = the mean of the x distribution, and σ = the standard deviation of the x distribution. Even if the x distribution is not normal, if the sample size n is sufficiently large ( n ? < ≥ 30 in most cases), the central limit theorem tells us that the x distribution is approximately ---Select--- binomial normal poisson geometric , the mean of the x distribution is μx = c , and the standard deviation of the x distribution is σx = c . (d) List at least three areas of everyday life to which the above concepts can be applied. Be specific. This answer has not been graded yet.

Answer 1

(a) (i)A population is the complete set of measurements from every individual of interest .

for example:If our interest is to find the average height of male football players in USA

then population is the height of all male football players in USA

(ii) A simple random sampling  is accomplished by assigning numbers to every member of the population , then using a table , calculator or computer to select random numbers from numbers assigned to population

example :Using a random number table to a draw a sample observation of height of all registered football players of USA.  

(b) A sample statistic is the numerical descriptive measure of a subset of complete set of measurements from every individual of interest .

for example sample mean is a sample statistic , which is calculated from sample observation .

Mean height of a sample of football players .

A sampling distribution is a probability distribution of sample statistic based on on possible simple random sample of same size from same population

example : the sampling distribution of sample mean is based on sample means of all possible samples drawn from the population of interest.

If we draw all possible sample of size n  from the population of football players of USA and then find the mean of all samples, then distribution  of these sample means is known as sampling distribution of sample means.

(c) The central limit theorem tells us that the x distribution is approximately normal , the mean of x distribution is

equal to  population mean and the standard deviation of x distribution is population s.d / square root of n

(d) Household income, exit poll results , test grades, clinical trial results are skewed distributions (not normal)

so if we take all possible samples of size greater than 30 and calculate the sample means for all samples

then distribution of sample mean follow normal with mean = population mean and standard deviation = population sd / sqrt(n)