Homework answers / question archive / For this Assignment, you are working at a firm that conducts independent testing for heavy industry

For this Assignment, you are working at a firm that conducts independent testing for heavy industry

Math

Share With

---

For this Assignment, you are working at a firm that conducts independent testing for heavy industry. Recently, an automobile manufacturer has been in the news for complaints about the highway gas mileage of their latest model minivan. You receive a contract from a consumer action group to test and write a report on the company’s claim that its minivans get 28 miles per gallon on the highway. The car company agrees to allow you to select randomly 35 low-mileage fleet minivans to test their highway mileage. Your test results gave you the following data:

29.7 24.5 27.1 29.8 29.2 27.0 27.8 24.1 29.3

25.9 26.2 24.5 32.8 26.8 27.8 24.0 23.6 29.2

26.5 27.7 27.1 23.7 24.1 27.2 25.9 26.7 27.8

27.3 27.6 22.8 25.3 26.6 26.4 27.1 26.1

To prepare for this Assignment:

Review this week’s Learning Resources.

Refer to your Week 4 Assignment in order to complete the Conclusion section of this Assignment.

Refer to the Academic Writing Expectations for 2000/3000-Level Courses as you compose your Assignment.

By Day 7

Submit Part 2 of your report (including the Conclusion) according to the following prompts.

Part 2: Hypothesis Testing: Two-Tail Test and One-Tail Test

Complete the following and include your results and responses in your report (use alpha = 0.05):

List the null and alternative hypotheses for the two-tail test for the mean. Calculate the observed value of the test statistic and the associated p-value. (75–150 words, or 1–2 paragraphs)

Is the observed test statistic in the critical region? Is the p-value higher or lower than your alpha? (75–150 words, or 1–2 paragraphs)

Note: Include your calculations. If your calculations are submitted separately, make note of where they can be found.

List the null and alternative hypotheses for the one-tail test of the mean. Calculate the observed value of the test statistic and the associated p-value. (75–150 words, or 1–2 paragraphs)

Is the observed test statistic in the critical region? Will the p-value be higher or lower than your alpha? (75–150 words, or 1–2 paragraphs)

Note: Include your calculations. If your calculations are submitted separately, make note of where they can be found.

Conclusions

In your report, use the confidence interval information and the results of the hypothesis testing to provide support for your conclusions and recommendations to the company. Specifically:

What conclusions did you reach? What did you learn about the situation by using each method? Did one method offer more conclusive proof than another? (150–225 words, or 2–3 paragraphs)

Based on your results, do you support the company’s claim that their minivans get 28 miles per gallon? (75 words, or 1 paragraph)

Summarize the details of your test methods and the results from each statistical method you used. Explain the findings so that executives from both the agency and the company can understand your conclusion. (150–225 words, or 2–3 paragraphs)

Finally, present recommendations for actions that the company might take to use your findings to better serve their customers in the future. (75 words, or 1 paragraph)

 

Week 5 Assignment Template: Minivan MPG Report Prepared by: Replace this text with your name. Date: Replace this text with the submission date. Walden University Part 2 (Hypothesis Testing: Two-Tail Test and One-Tail Test) Calculating a Two-Tail Test Replace this text with your response to the following in 75–150 words (1–2 paragraphs): List the null and alternative hypotheses for the two-tail test for the mean. Calculate the observed value of the test statistic and the associated p-value. Include your calculations. If your calculations are submitted separately, make note of where they can be found. Interpreting the Two-Tail Test Replace this text with your response to the following in 75–150 words (1–2 paragraphs): Is the observed test statistic in the critical region? Is the p-value higher or lower than your alpha? Calculating a One-Tail Test Replace this text with your response to the following in 75–150 words (1–2 paragraphs): List the null and alternative hypotheses for the one-tail test of the mean. Calculate the observed value of the test statistic and the associated p-value. Include your calculations. If your calculations are submitted separately, make note of where they can be found. Interpreting the One-Tail Test Replace this text with your response to the following in 75–150 words (1–2 paragraphs): Is the observed test statistic in the critical region? Will the p-value be higher or lower than your alpha? Part 3 (Conclusions) Methods Replace this text with your response to the following in 150–225 words (2–3 paragraphs): What conclusions did you reach? What did you learn about the situation by using each method? Did one method offer more conclusive proof than another? The Manufacturer’s Claim Replace this text with your response to the following in 75 words (1 paragraph): Based on your results, do you support the company’s claim that their minivans get 28 miles per gallon? Summary Replace this text with your response to the following in 150–225 words (2–3 paragraphs): Summarize the details of your test methods and the results from each statistical method you used. Explain the findings so that executives from both the agency and the company can understand your conclusion. Page 2 of 3 Recommendations Replace this text with your response to the following in 75 words (1 paragraph): Finally, present recommendations for actions that the company might take to use your findings to better serve their customers in the future. Attachments If applicable, list the filenames of any separate files you used to perform calculations. If you have no attachments, then indicate that in this section. Make sure that the file naming structure in this section matches the actual file names. References Include appropriately formatted references to at least one scholarly source for each prompt to support the statements made in your report. Please refer to the Writing Checklist for more information. Page 3 of 3 Assignment: Testing a Manufacturer’s MPG Claim: Part 2 • • • Note: Last week, you submitted Part 1 of this Assignment. This week, you will complete and submit only Part 2 (including the Conclusion). Companies often develop and test hypotheses about their products. For example, car manufacturers will test their cars to determine fuel efficiency and miles per gallon. To ensure that products are safe and that they perform as advertised, regulatory and consumer protection groups also test companies’ claims. For this Assignment, you are working at a firm that conducts independent testing for heavy industry. Recently, an automobile manufacturer has been in the news for complaints about the highway gas mileage of their latest model minivan. You receive a contract from a consumer action group to test and write a report on the company’s claim that its minivans get 28 miles per gallon on the highway. The car company agrees to allow you to select randomly 35 low-mileage fleet minivans to test their highway mileage. Your test results gave you the following data: 29.7 24.5 27.1 29.8 29.2 27.0 27.8 24.1 29.3 25.9 26.2 24.5 32.8 26.8 27.8 24.0 23.6 29.2 26.5 27.7 27.1 23.7 24.1 27.2 25.9 26.7 27.8 27.3 27.6 22.8 25.3 26.6 26.4 27.1 26.1 To prepare for this Assignment: Review this week’s Learning Resources. Refer to your Week 4 Assignment in order to complete the Conclusion section of this Assignment. Refer to the Academic Writing Expectations for 2000/3000-Level Courses as you compose your Assignment. Submit Part 2 of your report (including the Conclusion) according to the following prompts. Part 2: Hypothesis Testing: Two-Tail Test and One-Tail Test • o o • o Complete the following and include your results and responses in your report (use alpha = 0.05): List the null and alternative hypotheses for the two-tail test for the mean. Calculate the observed value of the test statistic and the associated p-value. (75–150 words, or 1–2 paragraphs) Is the observed test statistic in the critical region? Is the p-value higher or lower than your alpha? (75–150 words, or 1–2 paragraphs) Note: Include your calculations. If your calculations are submitted separately, make note of where they can be found. List the null and alternative hypotheses for the one-tail test of the mean. Calculate the observed value of the test statistic and the associated p-value. (75–150 words, or 1–2 paragraphs) Is the observed test statistic in the critical region? Will the p-value be higher or lower than your alpha? (75–150 words, or 1–2 paragraphs) o Note: Include your calculations. If your calculations are submitted separately, make note of where they can be found. Conclusions • • • • • • • In your report, use the confidence interval information and the results of the hypothesis testing to provide support for your conclusions and recommendations to the company. Specifically: What conclusions did you reach? What did you learn about the situation by using each method? Did one method offer more conclusive proof than another? (150–225 words, or 2–3 paragraphs) Based on your results, do you support the company’s claim that their minivans get 28 miles per gallon? (75 words, or 1 paragraph) Summarize the details of your test methods and the results from each statistical method you used. Explain the findings so that executives from both the agency and the company can understand your conclusion. (150–225 words, or 2–3 paragraphs) Finally, present recommendations for actions that the company might take to use your findings to better serve their customers in the future. (75 words, or 1 paragraph) • Note: If applicable, include any files that show your calculations. Make sure that the file naming matches what you have referenced in the report. Note: For each prompt, be sure to reference at least one scholarly source to support your answer. Use the Week 5 Assignment Template, provided in this week’s Learning Resources, to complete this Assignment. https://class.content.laureate.net/daf36ce0249b2d72f3357174364d328b.pdf https://class.content.laureate.net/4102437b9fd319fbdb0196e75e5503bf.pdf https://www.youtube.com/watch?v=5D1gV37bKXY&t= https://class.content.laureate.net/b754e58fcf47d125f942ae5a0779bbad.xlsx https://www.youtube.com/watch?v=0zZYBALbZgg https://class.content.laureate.net/a873443a15866f421d5dde49bc560dae.pdf Week 4 Assignment Template: Minivan MPG Report Prepared by: Clyde M. Singleton Date: 9th May, 2021 Walden University Introduction Car manufacturers conduct tests to determine fuel efficiency and mileage per gallon. Following the complaints about highway gas mileage of the latest model minivan, I receive a contract to test and report on the company’s claim that its minivans get 28 miles per gallon on the highway from a random sample of 35 low-mileage fleet minivans. Part 1: Sample Mean, Standard Deviation, and Confidence Interval Calculating the Confidence Interval For both dichotomous and continuous variables, the confidence interval—that is, CI, is a range of likely values of the population parameter based on the point estimate, level of confidence and sampling variability (Sullivan, n.d.). To find the 95% confidence interval we need to obtain the mean and standard deviation of the sample. Sample Mean(x?) = Sum of the results/n=35 (29.7+24.5+---+ 27.1+26.1)/35= 935.2/35= 26.72 The standard deviation is the square root of the variance which is obtained by: Square root {(29.7-26.72)2+ ... + (26.1 - 26.72)2}/34= square root (4.4116470588235 = 2.1003921202536 We use the t distribution table with 34 df α = 1 - c = 1 - 0.95 = 0.05; So tc = critical t value = "=TINV (0.05,34)" = 2.032245 The margin of error = E = tc∗s/ root (n)= (2.032245∗2.100392)/ root (35) = 0.72151 sample mean = x? = 26.72 Lower limit = x? - E = 26.72 - 0.72151 = 25.99849 Upper limit = x? + E = 26.72 + 0.72151 = 27.44151 Therefore, the 95% confidence interval of the true mean= (25.99849, 27.44151) Interpreting the Confidence Interval The correct interpretation of a 95% confidence interval is that "we are 95% confident that the population parameter is between X and X” (“Interpreting Confidence Intervals,” n.d.). For that reason, the answer in No. The company’s claimed mean is 28, which is not within the interval (25.99849, 27.44151) It is worth noting that “a specific confidence interval gives a range of plausible values for the parameter of interest” (“Interpreting confidence levels and confidence intervals,” n.d.) The upper limit of the confidence interval is 27.44151, which is less that the claimed mean of 28. Therefore, the value indicates that minivans get less that 28 miles per gallon on the highway. Page 2 of 3 References 4.2.1 - Interpreting Confidence Intervals | STAT 200. (n.d.). PennState: Statistics Online Courses. https://online.stat.psu.edu/stat200/lesson/4/4.2/4.2.1 Interpreting confidence levels and confidence intervals (article). (n.d.). Khan Academy. https://www.khanacademy.org/math/ap-statistics/estimating-confidence-ap/introductionconfidence-intervals/a/interpreting-confidence-levels-and-confidence-intervals Sullivan, L. (n.d.). Confidence Intervals. Sphweb.bumc.bu.edu. https://sphweb.bumc.bu.edu/otlt/MPHModules/BS/BS704_Confidence_Intervals/BS704_Confidence_Intervals_print.html