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QUESTION
Choose one design method from the list below. Using your example, make a list of 2 or 3 advantages and 2 or 3 disadvantages for using the method. (2 pts)
Simple random sampling
Systematic sampling
Stratified sampling
Cluster sampling
The name of each student in a class is written on a separate card. The cards are placed in a bag. Three names are picked from the bag. Identify which type of sampling is used and why. (2 pts)
A phone company obtains an alphabetical list of names of homeowners in a city. They select every 25th person from the list until a sample of 100 is obtained. They then call these 100 people to advertise their services. Does this sampling plan result in a random sample? What type of sample is it? Explain. (2 pts)
The manager of a company wants to investigate job satisfaction among its employees. One morning after a meeting, she talks to all 25 employees who attended. Does this sampling plan result in a random sample? What type of sample is it? Explain. (2 pts)
An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects 10 schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? What type of sample is it? Explain. (2 pts)
Fifty-one sophomore, 42 junior, and 55 senior students are selected from classes with 516, 428, and 551 students respectively. Identify which type of sampling is used and explain your reasoning. (2 pts)
You want to investigate the workplace attitudes concerning new policies that were put into effect. You have funding and support to contact at most 100 people. Choose a design method and discuss the following:
Describe the sample design method you will use and why. (2 pts)
Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.? (2 pts)
Discuss the bias, on the part of both the researcher and participants. (2 pts)
A local newspaper wanted to gather information about house sales in the area. It distributed 25,000 electronic surveys to its readers asking questions about house sales in the past 6 months. Of the surveys sent out, 3.2% were returned. The results found that 92% of people did not sell their house in the past 6 months and 85% of people would expect a loss if they sold their house. The writer wants to use these results to conclude that the housing market is declining, and we are headed for a recession.
Explain the bias and sampling error in this study. (2 pts)
Should the writer conclude that the housing market is declining based upon this data? (2 pts)
Why or why not? (2 pts)
A homeowner is getting carpet installed. The installer is charging her for 250 square feet. She thinks this is more than the actual space being carpeted. She asks a second installer to measure the space to confirm her doubt. Write the null hypothesis Ho and the alternative hypothesis Ha. (2 pts)
Drug A is the usual treatment for depression in graduate students. Pfizer has a new drug, Drug B, that it thinks may be more effective. You have been hired to design the test program. As part of your project briefing, you decide to explain the logic of statistical testing to the people who are going to be working for you.
Write the research hypothesis and the null hypothesis. (2 pts)
Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II error. (2 pts)
Write a paragraph explaining which error would be more severe, and why. (2 pts)Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variation from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces):
5.95
6.10
5.98
6.01
6.25
5.85
5.91
6.05
5.88
5.91
Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle?
State the hypothesis you will test. (2 pts)
Calculate the test statistic. (2 pts)
Find the P-value. (2 pts)
What is the conclusion? (2 pts)
Calculate a Z score when X = 20, μ = 17, and σ = 3.4. (2 pts)
Using a standard normal probabilities table, interpret the results for the Z score in Problem 12. (2 pts)
Your babysitter claims that she is underpaid given the current market. Her hourly wage is $12 per hour. You do some research and discover that the average wage in your area is $14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not. (2 pts)
Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is μ=350 and σ=35. The 100 students who completed the tutoring program had an average score of 385 points.
Is the students’ average score of 385 points significant at the 5% and 1% levels to support Tutor O-Rama’s claim of at least a 50-point increase in the SAT score? (2 pts)
Is the Tutor O-Rama students’ average score of 385 points significantly different at the 5% and 1% levels from the average score of 350 points on the math portion of the SAT? What conclusion can you make, based on your results, about the effectiveness of Tutor O-Rama’s tutoring? (2 pts)
| Subject | Statistics | Pages | 11 | Style | APA |
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Answer
Statistics Project
Question 1
- Simple random sampling – This is a sampling technique wherein every single member of the population has an equal opportunity of being selected as in forming a sample. The selection is purely random.
Systematic sampling – This is a sampling technique wherein elements are selected from a population based upon a predetermined pattern from a well-ordered list.
Stratified sampling – A sampling technique wherein a population is first segmented into smaller groups based upon certain parameter(s).
Cluster sampling – A sampling technique wherein a population in divided naturally into groups before a random sample from the population is chosen. This technique is employable when a researcher has no access to a whole population.
- Of the above, the chosen sampling technique for consideration is stratified sampling.
- Advantages of stratified sampling:
- The cost for every observation made is largely less
- Approximations of the parameters are can be produced for each and every subgroup
- Accuracy is characteristically better relative to simple random sampling since the probabilistic tactic ensures sample validity and minimizes human biases and is evenly spread to ensure greater level of precision
- Disadvantages of stratified sampling
- Not easy or practical to implement compared to cluster sampling in several instances and is more intricate compared to simple random sampling
- Requires the use of a complete list of a population and the population must vividly be delineated with no member being capable of fitting into two distinct subgroups
- It may be hard and challenging and time consuming to achieve a complete list of a targeted population
Question 2
Simple random sampling; each student in the class has equal to be selected
Question 3
Yes, the sampling plan results in a random sample. This is a systematic random sampling technique since the population is first sorted alphabetically.
Question 4
No, the sampling plan does not result in a random sample. This is because the employees who never attended the meeting did not have a chance of being selected and the attendance of the employees at the meeting was not decided randomly. Simply put, the employees who attended the meeting cannot represent the whole population at large. The sampling technique employed in the case, therefore, is convenience sampling since the manager only talked to the employees who attended the meeting.
Question 5
No, the sampling plan does not result in a random sample. The technique is cluster sampling since all teachers within the identified district are naturally partitioned into groups and that a set of subgroups was chosen, and all the members of the subgroups’ populations were sampled.
Question 6
The sampling technique that I would employ is stratified sampling. In a stratified sampling technique, a population is divided first into classes/strata before the strata are separately sampled. In the case, a tenth of each of the classes is sampled. Nonetheless, owing to the fact that freshmen are excluded, which may be a misemployment depending upon whether we are considering the freshmen as part of the targeted population. Applied rightly, classes must both be exhaustive and exclusive.
Question 7
- I would employ stratified random sampling. To begin the process, I would segment the employees into groups by gender from which classes I would select participants from the defined groups. I would then email the anonymous survey questionnaires to the participants. I would prefer stratified random sampling over simple random sampling technique since it generates extra accurate approximations of the characteristics of the population under study and provides intuition into any possible dissimilarity between the classes in a population.
- All the employees in the organization will form the study population. The sample group for the same is a group of people selected to complete the study questionnaires. I would do all that is possible to include all employees in the study.
- Bias can interplay in the study both from the researcher and participants’ sides. Participant bias is hard to surmount in the case scenario provided since dissatisfied employees may be adamant to share the right information and honest for retaliation fears. If the survey is noncompulsory, the less engaged workers will have high chances of participating in the survey relative to the busy ones. The study design can help minimize this kind of bias to a give degree despite being difficult to entirely eliminate.
Question 8
- The described survey is a not a random sample, but voluntary sample, making it be susceptible to various forms of biases. First, individuals having a robust opinion regarding the study topic have higher likelihood of responding relative to those with weak opinions. Similarly, the researcher exposes the study to bias by only sampling those who did subscribe to the newspaper. Similarly, the proportion of the population that did return the survey, 3.2%, was very low, while the 92% who returned the survey indicated that they did not sell their houses. With the small percentage that returned their surveys, the study is skewed towards individuals not selling their houses without taking into consideration others who did not get the surveys in the first place.
- this is because the study fails to provide enough and robust evidence either to refute or support the assertion that the housing market is declining. Similarly, biasness characterized the study right from the start since the researchers only sent the surveys to individuals who did subscribe to the newspaper, besides the very small number of surveys that were returned.
Question 9
Ho= The average carpeted space is ≤ 250 square feet
Ha: The average carpeted space is > 250 square feet
Question 10
- Ho: Drug B is substantially not extra effective than drug A
Ha: Drug B is substantially extra effective than drug A
- Type I and Type II error interplay
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OUR DECISION |
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Ho holds (Drug B is not substantially extra effective compared to drug A) |
H1 holds (Drug B is substantially extra effective compared to Drug A) |
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Question 11 Going by the information in the table, type I error would be extra severe owing to the fact that we are less informed about Drug B’s side effects besides the fact that it can be costlier compared to Drug A. having no information regarding Drug B’s side effects can have severe implications at students’ expense. Conversely, Drug A has previously been tried and tested on patients and proved just as effective as Drug B, making it a safer option. 5.91 Question 12
H1: The average amount of medicine in each bottle ≠ 6 ounces (µ≠6)
Z = = = = 5.989 n = 10, µ = 6 But test statistic (t) = , where m = mean, µ = theoretical value, s = standard deviation, and n = variable set size Thus, t = = -0.11595018087
p-value = P(IZI > 0.1159550181) = 0.907692025
We proceed to infer that we fail to reject the Ho owing to the fact that the p-value is > 0.05. Thus, there is insufficient proof to infer that the bottles are not filled according to label indicating 6 ounces.
Z score =, where z = standard score, x = observed value, σ = standard deviation, and μ = mean of the sample Therefore, Z-score = = 0.88235
P{Z < 0.88235) = 0.8112, implying that 81.12% of the values are ≤ the 20 x-value. Question 13
But x =12; µ = 14; δ = 1.9 Therefore, Z = = -1.0526
Z-score = -1.0526
P (Z < -1.0526) = 0.1463, implying that 14.63% (approx.. 15%) of the babysitters in the population under study are paid ≤ $12 per hour. Owing to the fact that that is what the babysitter is earning, there is no sufficient reason for raising it. Question 14 We formulate the following hypotheses: H0: The Student’s mean score is ≤ 350 points H1: The students’ mean score is > 350 points The test statistic (t) = Where x= 385, δ= 35, n =100, μ=350 Thus, Z = = 10.000 From the calculation above, I will fail to reject the Ho owing to the fact that the p-value is greater than the 1% and 5% levels of significance. The implication is that the average score for the students of 385 is statistically significant both at 1% and 5%. Tutor O-Rama’s assertion that their service will result in a rise in students SAT scores at worst 50 is incorrect.
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Ho holds (Drug B is not substantially extra effective compared to drug A) |
No error |
Type II error Drug B is not considerably extra effective compared to Drug A. However, in actual sense, this is not true. |
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