Cluster Sampling: Definition, Types, and Examples

Question 1 

Cluster Sampling 

For this method, we divide the population into clusters. What follows is random sampling. Finally, a survey is done for the sampled clusters. 

Advantages of Cluster Sampling 

It is considered more economical than stratified sampling and different design methods that incorporate the entire population. 

Cluster sampling is simple for a large population; for example, surveys done for the entire country. 

Cluster sampling becomes efficient due to less time required to conduct. 

Disadvantages of Cluster Sampling 

It offers inaccurate results for clusters with different population sizes. 

Due to the random selection of clusters, any slight error in cluster selection can lead to poor output. 

There is no full representation of a particular population. 

Question 2 

Since each student's name is drawn randomly and has an equal chance of being selected, then the method is simple random sampling. 

Question 3 

The method is systematic random sampling. The method is used where sampling members from a given population is done by choosing participants with a fixed interval. Hence, a random sample is created. 

Question 4 

The method is convenience sampling. No result is achieved in a random sample for the sampling plan as it involves a ready population. Therefore, this type of sampling fails to incorporate probability. 

Question 5 

The sampling method is cluster sampling. No result is achieved in a random sample for the sampling plan as it involves the population's sub-portion. Cluster sampling is regarded as convenient in scenarios when both heterogeneous and homogeneous cluster traits are visible in the population. 

Question 6 

The sampling method is stratified sampling since the final sample has a proportional representation of each class. Here we find that approximately 10% of each class is selected. 

Question 7 

The current situation requires a stratified sampling technique. The significant departments, that is, Human Resource, Logistics, Sales, Finance and Agriculture will form the strata. Inputs from the different departments will be selected to get the new policies' overall view of attitude. Samples will be selected randomly from each department, depending on the size of the department. For instance, if there are five departments with sizes (50, 75, 100, 25, 50), then the sample sizes for each of them will be (10, 15, 20, 5, 10), respectively. 

The entire employees will be the population, and the various departments will be the sample groups. There is no need to include every employee. Since part-time employees do not spend most of their time with the company, they may not have much exposure to the policy and knowledge of its implications. Therefore, full-time employees should be preferred. 

The bias of this survey is that some departments, particularly the Human Resource, may favor the policy since they are the ones who have implemented it. Another bias is when the investigation is direct. If the surveyed person's identity is open, they may choose not to reveal their true views; they may choose to provide only positive comments. 

Question 8 

The sampling method described here is a voluntary sampling. Therefore, there are chances of bias since the respondents are only those who have a strong opinion about the topic. There is a bias on the researcher's part since he only sampled the population that subscribed to the newspaper. The case separates the population into those that read the news, which does not represent the entire population. The young population which uses electronic media is eliminated from the survey. Since only 3.2% returned the survey and 92% of that 3.2% indicated they did not sell their house, this indicates a response bias that the majority of respondents have not sold a house. There is no clear idea if the other 96.8% of people who did not return the survey sold a house or even made money on selling a house, which is a large portion of the surveyed population to discount in the results. 

No. The survey does not provide sufficient evidence to support the claim. Therefore, the writer should not conclude that the housing market is declining. 

Question 9 

Question 10 

 : The effectiveness of drug B is equal to the effectiveness of drug A. 

 : The effectiveness of drug B is greater than the effectiveness of drug A. 

1.  

		Actual Effectiveness of Drugs
		No difference between A and B	B is better than A
Predicted effectiveness	No difference between A and B	No error	Type I error: Do not detect a difference, but B is really better than A. could result in lost profit.
	B is better than A	Type II error: Claim B is better, but there is really no difference. Could result in wasted costs developing and marketing drug B.	No error

Both errors can be severe. If the drug is a very important product in the marketplace, then perhaps the Type I error is more severe. This is because the Type I error may go forever unknown, as they abandon research on a drug that would have been a huge profit center for the company. On the other hand, the Type II error would likely result in more money spent readying the drug for the market. Then its lack of increased effectiveness could well be caught in subsequent trials. Even if not, it would probably have reasonable sales at first until its lack of effectiveness was eventually borne out from increased statistics. 

Question 11 

Hypothesis 

 . 

The test statistic for the mean is the z score. 

Where: 

 is the mean of  samples 

 is the population standard deviation 

 is the population mean 

P-value 

We fail to reject the null hypothesis because the obtained p-value is greater than the significance level. Therefore, we do not have sufficient evidence to conclude that the bottles are inadequately filled. 

Question 12 

From standard normal distribution table  can be interpreted as: 

This implies that there 18.88% probability that the value of 20 or greater would occur by chance, and 37.76% chance that a value with a difference of 3 or more from 17 would occur by chance. 

Question 13 

At the rate of $12/hr, she is being underpaid by slightly more than 1 standard deviation from the typical babysitter. At this level, there are only 14.63% of the babysitters that are paid less than she is. I would give her a raise. 

Question 14 

P-value =P(z<-4.286) 

Since the P value is less than the significance level  and 0.05 we reject the null hypothesis at both significance levels. We can conclude that there is insufficient evidence to support the claim that the service of Tutor O-Rama will raise the student SAT math scores to at least 50 points. 

The p-value is larger than the significance levels for 1% and 5 %. I this case, I will fail to reject the null hypothesis and conclude that the average score of 385 points is significant at 5% and 1% significance levels. Researcher’s claim that the Tutor services will raise SAT math scores at least 50 points is not true. 

References 

1. Akobeng, A. K. (2016). Understanding type I and type II errors, statistical power and sample size.  Acta Paediatrica ,  105 (6), 605-609. 

2. Taherdoost, H. (2016). Sampling methods in research methodology; how to choose a sampling technique for research.  How to Choose a Sampling Technique for Research (April 10, 2016) .