Question

please answer all parts of question, thank you so much

12. Identify the correct statements. Fix the incorrect ones.

a. A sampling distribution describes the distribution of data values.

b. A sampling distribution shows the behavior of a sampling process over many samples.

c. The probability distribution of a parameter is called a sampling distribution.

d. Sampling distributions describe the values of a data summary for many samples.

14. 14. Why is random sampling important?

18. A large university wants to send an exit survey to a SRS of 500 of its 3,827 graduating seniors. One question is, “Would you recommend to others that they should attend the university?” The response choices are: not sure, not likely, likely, definitely, most definitely. Describe how you would (in theory) use repeated sampling to obtain the sampling distribution of the sample proportion who would “definitely” or “most definitely” recommend the university to others.

Answer 1

12)

a) Incorrect

Reason:

Sample distribution is distribution of statistic like mean ,standard deviation of different samples have size n, for example if you want to find population mean , we will draw different samples with some samples randomly from that population like sample-1, sample-2, sample-3 ....so on

for each sample we will get corresponding mean if you plot distribution of these means that is called sample distributions

b)correct:

Reason:

In sample distribution we will not consider samples, we will consider sample statistic from different sample size,

we will pick many samples from population we will find statistic like mean from each sample,this statistic may or may not equal to true population mean.

c) Incorrect:

Reason:

In sample distribution we will not find parameter, we will find statistic

parameter term related to population

statistic term related to samples

so The probability distribution of a statistic(mean,sd) is called a sampling distribution

d)Incorrect:

Reason:

Sample distribution is distribution of statistic , it is not samples

below diagram is answer for all questions

14) 14. Importance Of random sampling:

Suppose if i want to find people in USA who are Indians , by select a sample how should i select?

if i select a sample by hand or by knowing person its like biased, that i'm asking the person role-model name that i already  known and that name i want.. how funny it is.

That means i;m completely biasing the solution, to avoid this we go for Random sampling.

How will do ?

a) simple random sampling:

The basic type i will write each person name with id in a paper and i will pick some piece of papers randomly in many papers, by this method i dont know the person , then there is no chance of bias answer.

b)Stratified Random Sampling:

The population divides into non-overlapping sub populations called strata.No applying simple random technique to every strata.

c) Cluster Sampling:

In cluster sampling we divide population is different clusters, each cluster has different samples unlike in strata may have homogeneous samples, but clusters have heterogeneous samples

18) Explanation:

Use stratified randomly sample in all department and school at different levels and the combine those samples into a final sample of size 500 to compute the sample proportion for those two categories mentioned.

There are 3827 graduate students no we will do make non overlapping sub populations called strata.each strata is based on some available information and done by some demographic variables like gender,age.

suppose in 3827 seniors we have different age group like 25-30,30-35,35-40 now we make strata(sample size) based on these age group it consist of all proportion, then internally the samples are homogeneous but externally each sample(strata) are different(non-overlapping) each other.

now we combine all these three strata into a final sample size 500 to compute the sample proportion of "definitely","most definitely"