Sampling and Sampling distributions

The post is about Online Sampling MCQs. There are 20 multiple-choice questions each with four possible options. The quiz covers the topics related to sample and sampling techniques, Types of Sampling Techniques, Sampling Frame and Sampling unit, and Sampling Error. Let us start with the Sampling MCQs Quiz.

Online Sampling MCQs with Answers

• Probability sampling is the procedure that gives all units
• Which of the following is not an example of a non-sampling risk?
• The advantage of using statistical sampling techniques is that such techniques
• Which of the following is an example of using statistical sampling?
• Which of the following is NOT one of the principles of sampling listed in the text?
• How is stratified sampling carried out?
• The sampling procedure that includes all units of the population in the study is called
• Why do sampling errors occur?
• If all other factors specified in an attribute sampling plan remain constant, changing the specified tolerable deviation rate from 6% to 10%, and changing the specified risk from 97% to 93%, would cause the required sample size to
• The sampling procedure in which an interviewer is asked to interview 25 teachers, 50 public servants, and 25 farmers are called
• A large retail store needs to conduct a survey to learn why their consumers purchase the store’s products. How should the retail store survey their customers?
• Data and business objectives might not align for a number of reasons. Which of the following issues can prevent alignment?
• A car manufacturer wants to learn more about the brand preferences of electric car owners. There are millions of electric car owners in the world. Who should the company survey?
• A restaurant gathers data about a new dish by providing free samples to parties of six or more diners. What does this scenario describe?
• Which of the following statements accurately describes a representative sample?
• What stage of the sampling process refers to creating a list of all the items in the target population?
• The instructor of a fitness class asks their regular students to take an online survey about the quality of the class. What sampling method does this scenario refer to?
• Which of the following activities are stages in the typical sampling process?
• In statistics, ———- refers to the number of individuals or items chosen for a study or experiment.
• The standard error measures the ———- of a sampling distribution.

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By determination of sample size, we mean to select the appropriate number of observations/ persons/ subjects from a large group to use in a sample. A sample with an appropriate number of observations and a sample with an appropriate size so that the results are statistically valid and accurate estimate the population parameters.

Importance of Determining the Sample Size

Determination of sample size is important as appropriate sample size usually saves time, costs, and labor involved in studying the members of the population. It also helps to select a representative sample of objects/subjects if an appropriate sampling technique is used for the selection of objects/subjects.

Therefore, it is important to remember that, a good sample size depends on the contexts and goals of the research being done. On the other hand, a good sample size results in reliable statistical estimates and represents the population under study accurately. In general, large sample sizes are considered better as they reduce the likelihood of sampling error. However, the larger the sample larger the time, cost, and labor required to collect the sample. The sample size directly affects the accuracy and reliability of your findings.

The margin of error will decrease by drawing a larger sample, for a given confidence level say $c$, standard deviation $\sigma$.

Determination of Sample Size and Sample Size Formula

One can determine the sample size if the maximum allowable error and level of confidence are known. If population standard deviation can be estimated, then the necessary sample size can be determined by simplifying the error formula for $n$.

The maximum allowable error is: $E=Z \frac{\sigma}{\sqrt{n}}$

By multiplying both sides with $\sqrt{n}$, we have

$E\sqrt{n} = Z \sigma$

Dividing both sides by $E$, we obtain $\sqrt{n} = \frac{Z\sigma}{E}$

Finally, squaring both sides, we get the sample size formula:
$$n=\left(\frac{Z\sigma}{E}\right)^2$$

Example: Determining Sample Size

Suppose, we are interested in finding the average weight of Pakistani men, and we want to be 95% confident that our estimate falls within $\pm2$lbs, of the actual mean. Let’s suppose that according to the previous studies, the population standard deviation (or estimated standard deviation) is $\sigma = 18.4$lbs. We are interested in determining sample size from the above-given information.

According to the given information
$\alpha = 0.05, Z_\alpha = 1.96$, the desired maximum error is $E=2$, and the estimated $\sigma = 18.4$. Therefore,
$$n=\left(\frac{Z\sigma}{E}\right)^2 = \left( \frac{1.96 \times 18.4}{2}\right)^2 \approx 325.15$$
The appropriate sample size for the above scenario should be 326 men for the given desired level of accuracy.

Summary

Note that If the population under study is highly diverse (heterogeneous population), a larger sample size may be necessary to ensure adequate representation of different subgroups. The type of study (e.g., survey, experiment) and the research questions can also influence the appropriate sample size. Similarly, the Practical Constraints: Factors such as budget, time, and accessibility can limit the feasible sample size.

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The post is about Multiple Choice Questions Related to Sampling and Sampling Techniques Quiz. There are 20 MCQs about Sampling Techniques covering the topics related, to stratified sampling, cluster sampling, and simple random sampling. Let us start with the Sampling Techniques Quiz.

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MCQs Sampling Techniques Quiz with Answers

• Sample allocation plan that provides the most precision, given a fixed sample size is
• In stratified random sampling with strata weights 0.35, 0.55, and 0.10, and standard deviations 16, 23, and 19, and sample sizes 70, 110, and 20, the variance of the sample mean estimator is?
• A group consists of 300 people and we are interviewing all members of a given group called
• When the procedure of selecting the elements from the population is not based on probability is known as
• Problem of non-Response
• If the respondents do not provide the required information to the researcher, then it is known as
• If larger units have more probability of their inclusion in the sample, the sampling is known as
• The cluster sampling method differs from the stratified sampling method in that
• One similarity between the stratified sampling method and the cluster sampling method is that
• In a cluster random sampling method
• In a stratified random sampling method
• Suppose that all the units in the population are divided into ten mutually exclusive groups. The word “mutually exclusive” means that
• When the population is badly affected, which type of sampling is appropriate?
• A randomly selected sample of 1000 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 1000 students surveyed said they had which one of the following statements about the number 0.16 is correct?
• Which ONE of the following is the main problem with using non-probability sampling techniques?
• Which of the following is not a characteristic of quota sampling?
• Before completing a survey, an individual acknowledges reading information about how and why the data they provide will be used. What is this concept called?
• ————- is a set of elements taken from a larger population according to certain rules.
• The mean of clusters average is the biased estimator of a population mean when
• Which of the following would usually require the smallest sample size because of efficiency?

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Online Sampling Distribution Quiz with Answers for the preparation of exams and different statistical job tests in Government/ Semi-Government or Private Organization sectors. This Online Quiz about Sampling Distributions is also helpful in getting admission to various colleges and Universities. There are 20 Multiple Choice Type Questions from the Sampling and Sampling Distribution Quiz. Let us start with the Sampling Distribution Quiz.

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MCQs Sampling Distribution Quiz with Answers

• The weight of the stratum is equal to the proportion of:
• A group consists of 300 people and we are interviewing all members of a given group called:
• When the procedure of selecting the elements from the population is not based on probability is known as:
• The university has 5000 students belonging to the following classes: (i) 1500 are freshmen, (ii) 1200 are sophomores, (iii) 1400 are juniors, and (iv) 900 are seniors. The university administration wants to get an estimate of all the student’s views on a proposal to help alleviate the parking problem on campus. Suppose, that a sample of 100 students is chosen, what is the required sample size for the freshman stratum under proportional allocation?
• When the sample size increases, everything else remains the same, and the width of a confidence interval for a population parameter will
• The value of $n_2$ by a proportional allocation from the following information is: $N_1=580$, $N_2=140$ and $n=80$.
• Sampling in which a sampling unit can be repeated more than once is called
• Which one of these sampling methods is a probability method?
• Which one of the following is the main problem with using non-probability sampling techniques?
• Which one of the following is the benefit of using simple random sampling?
• When sampling is done with or without replacement, $E(\overline{y})$ is equal to
• The margin of error is the level of ———- you require.
• If a researcher randomly samples 100 observations in each population category then his ————— sample will be ———-.
• Stratification is to produce estimators with small
• The weight of the stratum is equal to the proportion of
• When the number of observations drawn from a stratum is small relative to the overall size of the stratum then the ————- will also be small.
• Regardless of the difference in the distribution of the sample and population, the mean of sampling distribution must be equal to
• A procedure in which the number of elements in a stratum is proportional to the number of elements in the population is called
• Consider a population of size 700 consisting of three strata such that $N_1=100, N_2=250$, and $N_3=350$. The required sample size is 18. What will be the sample size for stratum-II according to proportional allocation?
• Consider a population of size 700 consisting of three strata such that $N_1=100, N_2=250$, and $N_3=350$. The required sample size is 18. What will be the sample size for stratum-III according to proportional allocation?

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A sampling distribution depends on several factors:

• The statistic being used: Is the researcher looking at the mean, median, or something else?
• The original population’s distribution: Is the population data normally distributed, skewed, or something else?
• Sample size: Generally, larger samples lead to sampling distributions closer to the actual population distribution.

In conclusion, sampling distributions are vital tools in statistics. Sampling Distributions help us to understand the variability of statistics calculated from samples and make informed inferences about the population from which the samples were drawn.