Grade = 100 Question Worth 1 2 3 4 5 Total 20 24 24 20 12 100 Points Lost 0 0 0 0 0 Hypothesis test for the True Proportion of Light Bulbs Broken in Packing/Shipping Question 1 , , Hypo , , Hypo Parameter Value Grader H0 : H1 : p p a Grader b Sample Statistics # Broken: x = 40 n= 1000 phat = SE = Hypothesis Test I/O a= 0.05 Z= p-value = Conclusion: Laymen's Conclusion Grader c d Grader e f g Grader h Hypothesis Test for the Mean , , Hypo Parameter H0 : H1 : , , m m b Hypothesis Test I/O a= df (if appropriate) = Test Stat = p-value = Conclusion: Laymen's Conclusion Sample Data: Grader a Grader Sample Statistics Mean = Std Dev = n= SE = Hypo Value c d e f g h i j k l Teabags 5.25 5.29 5.32 5.32 5.34 5.36 5.4 5.4 5.4 5.41 5.42 5.42 5.44 5.44 5.44 5.45 5.45 5.46 5.47 5.47 5.49 5.5 5.5 5.5 5.51 5.52 5.53 5.53 5.53 5.53 5.54 5.54 5.55 5.55 5.56 5.56 5.57 5.57 5.57 5.58 5.58 5.58 5.61 5.61 5.62 5.63 5.65 5.67 5.67 5.77 Grader m Hypothesis Test for the Mean , , Hypo Parameter H0 : H1 : , , m m b Hypothesis Test I/O a= df (if appropriate) = Test Stat = p-value = Conclusion: Laymen's Conclusion Sample Data: Grader a Grader Sample Statistics Mean = Std Dev = n= SE = Hypo Value c d e f g h i j k l Hospital data Patient 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 Grader m Hospital data Length 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 1 1 1 Hypothesis test for the Proportion , , Hypo Parameter H0 : H1 : , , p p b Hypothesis Test I/O a= 0.05 Z= p-value = Conclusion: Laymen's Conclusion Grader a Grader Sample Statistics x= n= phat = SE = Hypo Value Grader c d Grader e f g Grader h Part a , , Hypo Parameter , , Hypo Value Grader H0 : H1 : Part b , , Hypo Parameter H0 : H1 : , , Hypo Value Grader Do not enter anything in the spreadsheet cells that are black, labeled \"Grader\". DO NOT CHANGE THE APPEARANCE, FORMATTING, OR FUNCTIONALITY OF THE SPREADSHEET UNLESS INSTRUCTED TO DO SO. Question 1 As part of a supplier certification program, American Lighting Company's wholesale customers will not accept a shipment of bulbs from American if a random sample of bulbs taken at delivery indicates that more than 3% of bulbs are broken. As a result, the company has a \"Zero Breaks Shipped\" program to ensure the bulbs are not broken when they leave the plant. After the bulbs are packed for a wholesale customer, the program requires sampling 1000 bulbs from the lot to be shipped and check to see if any bulb is broken. A recent sample of 1000 bulbs revealed that 40 were broken. At the 5% significance level, perform the appropriate hypothesis test to determine if the shipment has more than the acceptable percentage of broken bulbs. Use the appropriate built-in Excel function or write a formula where appropriate, both of which should reference the proper cells in the worksheet. Follow parts a through h below to complete question 1. The number of broken bulbs and the sample size are provided in the worksheet named Lighting Co. a. b. c. d. e. f. g. h. 2 Points: In cells E4 & E5, input the value of the hypothesized proportion of broken bulbs (decimal form). 2 Points: In cells D4 & D5, input the appropriate equalities/inequalities ([=, ], [, >], [, <]) for the null and alternate hypothesis. 2 Points: In cell B11, calculate the proportion of bulbs in the sample of 1000 that were broken, referencing the appropriate cells. 2 Points: Calculate the standard error (SE) of the proportion in cell B12, referencing the appropriate cells. 3 Points: Calculate the test statistic, Z, in cell B17, referencing the appropriate cells. 3 Points: Calculate the p-value of the hypothesis test in cell B18 using a built-in Excel function that references the appropriate cells. 3 Points: In cell B19, write either the words \"Fail to Reject\" or \"Reject\" to indicate the appropriate conclusion based on the p-value. 3 Points: In cell A21, write a short layman's conclusion in terms of if the proportion of broken bulbs is more than 3%, and if the lot should or should not be shipped. Question 2 (Problem Scenario taken from Basic Business Statistics Concepts and Applications, eighth edition, by Berenson, Levine, and Krehbiel) A quality characteristic of interest for a tea-bag filling process is the weight of the tea in individual bags. If the bags are underfilled, two problems arise. First, customers may not be able to brew tea to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. For this scenario, the label weight on the package indicates that, on 1 average, there are 5.5 grams of tea in a bag. If the average amount of tea in a bag exceeds the label weight, the company is giving away the product. Getting the exact amount of tea in a bag is problematic because of variation in the temperature and humidity inside the factory, differences in the density of tea, and the extremely fast filling operation of the machine (approximately 170 bags a minute). The weights in grams of a sample of 50 bags produced during an eight-hour shift by a single machine are provided in the worksheet named Tea-bags. Is there evidence that the mean amount of tea per bag is different from 5.5 grams? Use a 0.01 level of significance. a. b. c. d. e. f. g. h. i. j. k. l. m. 1 Point: In cells E4 & E5, input the value of the hypothesized mean amount of tea per bag in grams. 2 Points: In cells D4 & D5, input the appropriate equalities/inequalities ([=, ], [, >], [, <]) for the null and alternate hypothesis. 2 Points: In cell B9, calculate the mean weight for the sample of 50 tea bags, referencing the appropriate cells. 2 Points: In cell B10, calculate the standard deviation of the weights for the sample of 50 tea bags, referencing appropriate cells. 1 Point: Compute the size is the sample in cell B11 using an Excel function. 2 Points: Calculate the standard error (SE) of the mean in cell B12, referencing the appropriate cells. 1 Point: Place the specified level of significance in cell B16. 1 Point: Compute the degrees of freedom placing the computation in cell B17. 2 Points: Calculate the value of the test statistic in cell B18, referencing the appropriate cells. 2 Points: Calculate the p-value of the hypothesis test in cell B19 using a built-in Excel function that references the appropriate cells. 2 Points: In cell B20, write either the words \"Fail to Reject\" or \"Reject\" to indicate the appropriate conclusion based on the p-value. 2 Points: In cell A22, write a short layman's conclusion. 4 Points: Verify your reults using StatTools. Place your StatTools output with an upper left hand cell in cell J4. 2 Question 3 The numbers of days 44 mothers spent in the hospital giving birth (after January 1, 2005) are given in the worksheet named Hospital Stay. Before insurance rules were changed (the change was effective January 1, 2005), the average number of days spent in a hospital by a new mother was 2 days. For a 0.05 level of significance, do the data indicate that women are now spending less time in the hospital after giving birth than they were prior to 2005? a. b. c. d. e. f. g. h. i. j. k. l. m. 1 Point: In cells E4 & E5, input the value of the hypothesized average number of days spent in a hospital by a new mother. 2 Points: In cells D4 & D5, input the appropriate equalities/inequalities ([=, ], [, >], [, <]) for the null and alternate hypothesis. 2 Points: In cell B9, calculate the mean number of days spent in a hospital by a new mother for the sample of 44 mothers, referencing the appropriate cells. 2 Points: In cell B10, calculate the standard deviation of the number of days spent in a hospital by a new mother for the sample of 44 mothers, referencing appropriate cells. 1 Point: Compute the size is the sample in cell B11 using an Excel function. 2 Points: Calculate the standard error (SE) of the mean in cell B12, referencing the appropriate cells. 1 Point: Place the specified level of significance in cell B16. 1 Point: Compute the degrees of freedom placing the computation in cell B17. 2 Points: Calculate the value of the test statistic in cell B18, referencing the appropriate cells. 2 Points: Calculate the p-value of the hypothesis test in cell B19 using a built-in Excel function that references the appropriate cells. 2 Points: In cell B20, write either the words \"Fail to Reject\" or \"Reject\" to indicate the appropriate conclusion based on the p-value. 2 Points: In cell A22, write a short layman's conclusion. 4 Points: Verify your reults using StatTools. Place your StatTools output with an upper left hand cell in cell J4. 3 Question 4 (Problem Scenario taken from Business Statistics by Sharpe, De Veaux, and Velleman) A nonprofit company concerned with the school dropout rates in the United States has designed a tutoring program aimed at students between 16 to 18 years old. The National Center for Education Statistics reported that the high school dropout rate in the United States for the year 2000 was 10.9%. One school district, who adopted the use of the nonprofit's tutoring program and whose dropout rate has always been very close to the national average, reported in 2004 that 175 of their 1782 students dropped out. Is their experience evidence that the tutoring program has been effective? Follow parts a through h below to complete question 4. Provide your support in the worksheet titled Nonprofit. a. b. c. d. e. f. g. h. 2 Points: In cells E4 & E5, input the value of the hypothesized proportion of school dropouts (decimal form). 2 Points: In cells D4 & D5, input the appropriate equalities/inequalities ([=, ], [, >], [, <]) for the null and alternate hypothesis. 2 Points: Input the values for x and n in cells B9 and B10, respectively. Then in cell B11, calculate the proportion of school dropouts in the sample of students, referencing the appropriate cells. 2 Points: Calculate the standard error (SE) of the proportion in cell B12, referencing the appropriate cells. 3 Points: Calculate the test statistic, Z, in cell B17, referencing the appropriate cells. 3 Points: Calculate the p-value of the hypothesis test in cell B18 using a built-in Excel function that references the appropriate cells. 3 Points: In cell B19, write either the words \"Fail to Reject\" or \"Reject\" to indicate the appropriate conclusion based on the p-value. 3 Points: In cell A21, write a short layman's. Question 5 (Problem Scenarios taken from Business Statistics by Sharpe, De Veaux, and Velleman) Place your answers in the worksheet titled Question 5. Provide the appropriate parameter symbol, equalities/inequalities, and hypothesized values. a. 6 Points: A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard deviation of 4.83 mpg. Is there strong evidence that they have failed to attain their fuel economy goal? Write appropriate hypotheses. b. 6 Points: An online clothing company is concerned about the timeliness of the delivery of their products. The VP of Operations and Marketing recently stated that she wanted the percentage of products delivered on time to be more than 90%, and she wants to know if the company has succeeded. Write appropriate hypotheses. 4 5