Problems Need To Include All Required Steps And Answers ✓ Solved

Problems Need To Include All Required Steps And Answers For Full

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible. Answer the following problems showing your work and explaining (or analyzing) your results.

1. 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

2. 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)

3. 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)

4. 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)

5. 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)

6. 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)

7. 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)

8. 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. 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)

9. 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)

10. 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. 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)

11. 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..........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)

12. Calculate a Z score when X = 20, μ = 17, and σ = 3.4. (2 pts)

13. Using a standard normal probabilities table, interpret the results for the Z score in Problem 12. (2 pts)

14. 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)

15. 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)

Paper For Above Instructions

This paper addresses the various sampling methods, their respective advantages and disadvantages, hypotheses, statistical calculations, and interpretations pertaining to sample studies and experimental designs as required by the given instructions.

1. Sampling Method: Stratified Sampling

Stratified sampling involves dividing a population into distinct subgroups (strata) and then randomly selecting samples from each stratum. The main advantages include:

• Increased Precision: By ensuring representation from each subgroup, stratified sampling often yields more reliable results.
• Comparison Between Groups: It allows for comparison among strata which can unveil differences that might be missed in nonspecific sampling methods.
• Resource Management: Focused sampling can help identify key insights relevant to specific segments of the population.

Disadvantages include:

• Complexity: The process can be more complicated and time-consuming than simple random sampling.
• Need for Accurate Strata Identification: If strata are wrongly defined, it can lead to biased results.
• Potential for Sample Size Imbalance: If stratum sizes are unequal, some may get overrepresented in results.

2. Type of Sampling Used: Simple Random Sampling

Picking names from a bag represents simple random sampling because each student has an equal chance of being chosen, ensuring that every individual in the class contributes to the outcome.

3. Type of Sample: Systematic Sampling

By selecting every 25th name from a list, this method illustrates systematic sampling. It is not entirely random due to reliance on a predetermined interval rather than truly random selection.

4. Type of Sampling: Convenience Sampling

This process does not yield a random sample because it only considers a subset of employees who attended one meeting. This can introduce bias based on who chooses to attend.

5. Type of Sampling: Cluster Sampling

Since all teachers in randomly selected schools are interviewed, this exemplifies cluster sampling. It might not represent all teaching methods across the district.

6. Type of Sampling: Stratified Sampling

This selection method targets specific student groups and draws from each, indicating stratified sampling. Each class level is treated as a stratum.

7. Chosen Method: Simple Random Sampling

The target population would encompass all employees within the company to ensure comprehensive representation and reduce biases. Although full-time and part-time distinctions could introduce variability in responses, focusing solely on engagement and input regarding workplace attitudes is crucial.

8. Bias and Sampling Error in Local Newspaper Study

The low return rate of responses from the distributed surveys can introduce significant bias, making it difficult to generalize the findings about the housing market. Without ensuring a comprehensive demographic representation, concluding that the housing market is declining could be misleading. Hence, the writer should not draw definitive conclusions based solely on this data.

9. Null and Alternative Hypotheses

Ho: The actual area being carpeted is less than or equal to 250 square feet.

Ha: The actual area being carpeted is greater than 250 square feet.

10. Research Hypothesis for Drug Trial

Ho: Drug B is not more effective than Drug A.

Ha: Drug B is more effective than Drug A.

Error Type	Description
Type I Error	Rejecting Ho when it is true (concluding Drug B is effective when it is not).
Type II Error	Failing to reject Ho when Ha is true (concluding Drug B is not effective when it actually is).

Type I errors can be more severe in clinical settings, as they may lead to the approval of ineffective treatments, putting patients at risk.

11. Hypothesis for Quality Assurance of Cough Syrup

Ho: The mean amount in the bottles is equal to 6 ounces.

Ha: The mean amount in the bottles is less than 6 ounces.

Test Statistic Calculation:

Using the sample data and applying the appropriate statistical test could determine whether the mean is significantly different from 6 ounces.

P-Value:

Obtaining this value will depend on the test conducted, indicating whether the results are statistically significant.

Conclusion:

Conclusions will be drawn from the comparisons, focusing on meeting the quality assurance standards that align with the expected mean volume.

12. Z Score Calculation

Z = (X - μ) / σ = (20 - 17) / 3.4 = 0.8824

13. Interpretation of Z Score

A Z score of 0.8824 indicates that the value of 20 is 0.8824 standard deviations above the mean. Consulting standard normal probability tables would yield the corresponding probabilities.

14. Z Score for Babysitter's Wage

Z = (12 - 14) / 1.9 = -1.05. Since this Z score is below 0, it indicates that the babysitter is earning less than the average wage, providing grounds for a raise.

15. Tutor O-Rama Performance Assessment

To determine whether the average score of 385 points significantly supports the claim of at least a 50-point increase, statistical tests such as t-tests would be applied against the set significance levels, considering the existing averages from before the tutoring. The conclusion would base on whether the results lie within the acceptable bounds of statistical significance.

References

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• Moore, D. S., & McCabe, G. P. (2006). Introduction to the Practice of Statistics. W.H. Freeman.
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