# Critical Value for Decision Making

Critical Value for Decision Making.

Instructions: The homework must be placed in the appropriate Assignments folder in Blackboard by midnight of the date shown in the Course Roadmap and Syllabus. The Assignments folder will close automatically and late submissions will not be allowed thus a score of zero (0) will be recorded for the assignment. Solutions for the assignment will be released in Bb the morning after the due date. Total points for the assignment is 80.

For the following criteria write the Ho and Ha hypotheses in the space provided.

1. The historical test average (or mean) on a Statistics test is 86. The Instructor thinks that a new teaching methodology will influence these test scores. (1 point each for a total of 2 points)

Ho:

Ha:

2. The historical test average (or mean) on a Statistics test is 74. The Instructor thinks that a new teaching methodology will increase these test scores. (1 point each for a total of 2 points)

Ho:

Ha

3. The historical test average (or mean) on a Statistics test is 92. The Department Chair thinks that the content of a new textbook may lower the test scores. (1 point each for a total of 2 points)

Ho:

Ha:

4. The historical test average (or mean) on a Statistics test is 65. A new teacher thinks that the content of a new textbook may raise these test scores. (1 point each for a total of 2 points)

Ho:

Ha:

5. The historical test average (or mean) on a Statistics test is 70. The teacher thinks that his teaching method will influence these test scores. (1 point each for a total of 2 points)

Ho:

Ha:
6. A textbook publisher claims the historical proportion of students passing the standardized statistics test is 77% using their textbook. The school districts Superintendent thinks the passing rate is more than 77%. (1 point each for a total of 2 points)

Ho:

Ha:

7. Disney World claims that 60% of the couples it admits bring children. As the Marketing Manager you think this percentage is incorrect, its not 60%. (1 point each for a total of 2 points)

Ho:

Ha:

8. The historical dropout rate for seniors in your high school is 8%. The school Principal claims the percentage is greater than 8%. (1 point each for a total of 2 points)

Ho:

Ha:

9. It was recently reported by the Humane Society that 15.7% of families in your county have a pet. However, you believe the proportion of families that own pets is different, its not 15.7%. (1 point each for a total of 2 points)

Ho:

Ha:

10. As a school administrator you have calculated that historically 90% of high school freshmen girls go out for JV cheerleading. However you think this percentage is low. You think more than 90% try out. (1 point each for a total of 2 points)

Ho:

Ha:

For the following scenarios write the Ho & Ha, identify the critical value (CV) used for the decision rule, calculate the z-value test statistic and state a conclusion. Write your answer in the spaces provided. You may use Excel, Ti-84 or the chart.

11. At the local community college it has been reported the average age of first year college students is 20 years of age with a standard deviation of 7.2 years. As a college professor you believe its less. To test your claim you take a random sample of 200 students, the average age 19.4 years. At an alpha of 0.02 what do you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
12. As the summer director of Exploratory Camp, you provide academic enrichment for students that scored poorly on the DCAS. Capital School District thinks the summer program will influence test scores in the fall. The historical average of summer mathematics assessments is 21.3 with a standard deviation of 5. To test the claim of the school district, you assess 80 students in mathematics. The sample average on the test is 20.03. At an alpha of 0.05 what can you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
13. Goodyear Tire and Rubber Company manufacture tires in North America. The daily production of the Eagle GT tire follows the normal distribution, with a mean of 200 and a standard deviation of 31. Recently, because of market expansion, new production methods have been introduced and new employees hired. The CEO of the company would like to investigate whether there has been a change in the weekly production of the Eagle GT and asks the Production Manager for the 180-day output report. The report stated that on average 205 tires were produced per day. At an alpha of 0.01 significance what can you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
14. The local newspaper recently reported that the average beverage bill at Phillips Crab House in Ocean City, Maryland is \$35 with a standard deviation is known to be \$9.58. As a wait-staff person you think its less than \$35. Therefore, you randomly sample 49 bar bills and calculate the average to be \$32.50. At an alpha of .02 what can we conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
15. A customer service representative for Comcast has just told you that the historical average for customers service call wait times is 4.21 minutes with a standard deviation of 5.2 minutes. As a Comcast customer, you do not trust the representatives claim because you believe the wait time is much longer than stated. To test the representatives claim (at an alpha of 0.05) you survey 817 Comcast customers who have recently called the customer service line and found the average to be 4.54 minutes. (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:

For the following scenarios write the Ho & Ha, identify the critical value (CV) used for the decision rule, calculate the p-value test statistic and state a conclusion. Write your answer in the spaces provided. You may use Excel, Ti-84 or the chart.

16. Your company reports that the historical average number of vacation days taken by full-time employees is 10.2 days per year with a standard deviation of 7.55 vacation days. You believe the average number of vacation days taken by full-time employees is lower. To test your claim you take a random sample of 121 employees at your company. You find the sample average to be 8.9 vacation days. At an alpha of 0.05 what can you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
17. Assume that you make candy bars; the advertised weight of the candy bar is 4 ounces with a standard deviation (s) of 2.35 oz. however your production manager thinks that this is not true; he thinks the candy bars are over-weight, they weigh more than 4 oz. To test his claim you decided to randomly select a sample of 126 candy bars, the average weight (x-bar) is 4.48 oz.. At an alpha () of 0.01 what do you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
18. Historically, according to the Graduate School Association, most graduate students attend schools within 70 miles of their homes with a standard deviation of 21.08 miles. You teach at WU in the Nursing Program and believe this is not true, you think the mileage is less than 70 miles. To test your hunch you conduct a study among 150 randomly selected students in the program and calculate that, on average, they live 74.31 miles from the campus. At an alpha of 0.10 what can you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
19. The historical age of high school seniors entering the local community college has been 21 with a standard deviation of 13.44, however as an academic counselor you think the actual age is different. To test your claim you randomly select a sample of 214 students and calculate their age. The average age of the 214 students is 19.5 years. At an alpha of 0.05 what can you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
20. As the owner of Teachdrive One driving academy you advertise that it takes new students an average of 12 days (with a standard deviation of 8.12 days) to learn how to parallel park. You have been observing the students and in addition to developing an irrational fear of driving on the same road as these students you believe that it is different. To test your claim, you randomly select a sample of 91 new student drivers and find that the average number of days is 14 At an alpha of 0.10 want can you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
For the following scenarios write the Ho & Ha, identify the critical value (CV) used for the decision rule, calculate the t-value test statistic and state a conclusion. Write your answer in the spaces provided.

21. The purchase of a coin-operated laundry is being considered by a potential entrepreneur. The present owner claims that over the past 5 years the average daily revenue has been \$675 with a standard deviation of \$110 but the potential buyer thinks it is less. A sample of 30 selected days revenue reveals a daily average revenue of \$625 with a sample standard deviation of \$110. Is there overwhelming evidence at the 0.05 level to support the Bureaus claim? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:
22. The Better Business Bureau has received several complaints that a flour company is lax in filling their five-pound bags of flour. They think the bags are under filled. The Bureau randomly selects 41 bags of flour and determines the weight of each bag. The sample average weight of the bags is 4.85 pounds with a standard deviation of 1.8 pounds. Is there overwhelming evidence at the 0.01 level to support the Bureaus claim? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:

23. Tomatoes are grown in Florida for shipment to other parts of the country by the Anderson Produce Company. The company wants to make certain its weighing process is in control and are not shipping out over or under weight boxes, therefore a random sample of 46 boxes is selected at one warehouse for weighing. The average weight for the sample is 33.5 pounds per box with a standard deviation of 3.9 pounds. The companys standard for tomatoes in this run is 33 pounds. At an alpha of 0.02 what do you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:

24. A pharmaceutical company produces a diet pill that if taken daily will reduce the appetite of the pill-taker. Research suggests that the average daily intake of calories is 1500 per day. However a random sample of 61 people (who agreed to test the product) revealed a mean calorie intake of 1490 calories per day with a standard deviation of 35 calories. At an alpha of 0.10 want can you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:

25. A microprocessor designer has developed a new fabrication process which he believes will change the life of a computer chip. Currently the usable life is 16,000 hours. A sample of 71 microprocessors was tested and had a mean life of 16,500 hours with a standard deviation of 2,500 hours. At an alpha of 0.10 want can you conclude? (1 point each for a total of 4 points)

Ho:

Ha:

Critical Value for Decision Making:

Calculated Test Statistic:

Conclusion:

Critical Value for Decision Making

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