calculate PART A PART B PART C:

PART A Express the confidence interval 74.3%±8.6%74.3%±8.6% in the form of a trilinear inequality.

% <p<<p< %

PART B: We wish to estimate what percent of adult residents in a certain county are parents. Out of 400 adult residents sampled, 44 had kids. Based on this, construct a 90% confidence interval for the proportion p of adult residents who are parents in this county.

Provide the point estimate and margin of error. Give your answers as decimals, to three places.

p =  ±±

PART C: You measure 50 textbooks' weights, and find they have a mean weight of 62 ounces. Assume the population standard deviation is 2.7 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

< μμ <

Two qualified inspectors are hired to inspect major vehicle components (transmission, engines, axle assemblies, and other large items). These employees will be the last personnel to look at any item before it is prepared for shipment. They are the last link in the manufacturing chain. One inspector (Mr. A) has been doing this type of work for nearly 15 years. The other person (Mr. B) is comparatively new, but still has developed a fine track record. He has been inspecting for two years. Nobody is perfect and occasionally a discrepancy or potential problem is missed. The likelihood that Mr. A performs a completely perfect inspection is .90. Mr. B has an 80% accuracy rate for inspecting. These inspectors operate independently in separate but similar areas in the pre-shipment zones of the company. However, each performs his own inspection on every item utilizing a two-man rule.

3. What is the likelihood that only one inspector performs a perfect inspection?

4. What is the chance that both inspectors missed discrepancies or problem areas that existed?

5. What is the chance that Mr. A missed a potential problem in his inspection given that Mr. B performed his perfectly?

1. A computer manager needs to know how efficiency of her new computer program depends on the size of incoming data. Efficiency will be measured by the number of processed requests per hour. Applying the program to data sets of different sizes, she obtains the following results,

Data size (gigabytes) 6 7 7 8 10 10 15

Processed requests 40 55 50 41 17 26 16

1. Draw the scatterplot for the data. Be sure to label your axes.

2. Is there any correlation between the processing request and the size of incoming data?

   What is the correlation coefficient?

3. By what percentage is the processing time dependent on the size of incoming data?

4. Compute a least square regression line for regressing processing request on the size of incoming data.

5. Use your regression equation to predict the processing request for an incoming data of size 17.0 gigabytes

6. Is the slope statistically significant at α = 5% ?

1. conic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table.

(a) Complete the F-table. (Round your values for MS and F to two decimal places.)

(b) Compute Tukey's HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two decimal places.)

The critical value is    for each pairwise comparison.

c) Which of the comparisons had significant differences? (Select all that apply.)

a. Recall following no delay was significantly different from recall following a one second delay.

b. Recall following a half second delay was significantly different from recall following a one second delay.

c. The null hypothesis of no difference should be retained because none of the pairwise comparisons demonstrate a significant difference.

d. Recall following no delay was significantly different from recall following a half second delay.

2. An educator wants to evaluate four different methods aimed at reducing the time children spend "off task" in the classroom. To test these methods, she implements one method in each of four similar classrooms and records the time spent off task (in minutes) in each classroom. The results are given in the table.

(a) Complete the F-table. (Round your answers to two decimal places.)

3. After computing a one-way within-subjects analysis of variance at a 0.1 level of significance, a psychologist begins to calculate a Bonferroni procedure. If she will make a 5 pairwise comparisons, what will be the testwise alpha?

Parts Emporium, Inc., is a wholesale distributor of automobile parts formed by two disenchanted auto mechanics, Dan Block and Ed Spriggs. Originally located in Block’s garage, the firm showed slow but steady growth for 7 years before it relocated to an old, abandoned meat-packing warehouse on Chicago’s South Side. With increased space for inventory storage, the company was able to begin offering an expanded line of auto parts. This increased selection, combined with the trend toward longer car ownership, led to an explosive growth of the business. Fifteen years later, Parts Emporium was the largest independent distributor of auto parts in the north central region. Recently, Parts Emporium relocated to a sparkling new office and warehouse complex off Interstate 55 in suburban Chicago. The warehouse space alone occupied more than 100,000 square feet. Although only a handful of new products have been added since the warehouse was constructed, its utilization increased from 65 percent to more than 90 percent of capacity. During this same period, however, sales growth stagnated. These conditions motivated Block and Spriggs to hire the first manager from outside the company in the firm’s history. It is June 6, Sue McCaskey’s first day in the newly created position of materials manager for Parts Emporium. A recent graduate of a prominent business school, McCaskey is eagerly awaiting her first real-world problem. At approximately 8:30 A. M., it arrives in the form of status reports on inventory and orders shipped. At the top of an extensive computer printout is a handwritten note from Joe Donnell, the purchasing manager: “Attached you will find the inventory and customer service performance data. Rest assured that the individual inventory levels are accurate because we took a complete physical inventory count at the end of last week. Unfortunately, we do not keep compiled records in some of the areas as you requested. However, you are welcome to do so yourself. Welcome aboard!” A little upset that aggregate information is not available, McCaskey decides to randomly select a small sample of approximately 100 items and compile inventory and customer service characteristics to get a feel for the “total picture.” The results of this experiment reveal to her why Parts Emporium decided to create the position she now fills. It seems that the inventory is in all the wrong places. Although an average of approximately 40 days of inventory is on hand, the firm’s customer service is inadequate. Parts Emporium tries to backorder the customer orders not immediately filled from stock, but some 12 percent of demand is being lost to competing distributorships. Because stockouts are costly, relative to inventory holding costs, McCaskey believes that a cycle-service level of at least 99 percent should be achieved. McCaskey knows that although her influence to initiate changes will be limited, she must produce positive results immediately. Thus, she decides to concentrate on two products from the extensive product line: the EG151 exhaust gasket and the DB032 drive belt. If she can demonstrate significant gains from proper inventory management for just two products, perhaps Block and Spriggs will give her the backing needed to change the total inventory management system. The EG151 exhaust gasket is purchased from an overseas supplier, Haipei, Inc. Actual demand for the first 21 weeks of this year is shown in the following table: Week Actual Demand Week Actual Demand Week Actual Demand 1 84 8 87 15 86 2 85 9 85 16 85 3 88 10 87 17 82 4 87 11 85 18 83 5 85 12 83 19 85 6 85 13 83 20 85 7 84 14 84 21 87 A quick review of past orders, shown in another document, indicates that a lot size of 500 units is being used and that the lead time from Haipei is fairly constant at 2 weeks. Currently, at the end of week 21, no inventory is on hand, 11 units are backordered, and the company is awaiting a scheduled receipt of 200 units. The DB032 drive belt is purchased from the Bendox Corporation of Grand Rapids, Michigan. Actual demand so far this year is shown in the following table: Week Actual Demand Week Actual Demand Week Actual Demand 11 16 15 45 19 48 12 29 16 47 20 43 13 47 17 44 21 45 14 48 18 47 Because this product is new, data are available only since its introduction in week 11. Currently, 324 units are on hand, with no backorders and no scheduled receipts. A lot size of 500 units is being used, with the lead time fairly constant at 3 weeks. The wholesale prices that Parts Emporium charges its customers are $12.50 for the EG151 exhaust gasket and $8.80 for the DB032 drive belt. Because no quantity discounts are offered on these two highly profitable items, gross margins based on current purchasing practices are 40 percent of the wholesale price for the exhaust gasket and 36 percent of the wholesale price for the drive belt. Parts Emporium estimates its cost to hold inventory at 20 percent of its inventory investment. This percentage recognizes the opportunity cost of tying money up in inventory and the variable costs of taxes, insurance, and shrinkage. The annual report notes other warehousing expenditures for utilities and maintenance and debt service on the 100,000-square-foot warehouse, which was built for $1.5 million. However, McCaskey reasons that these warehousing costs can be ignored because they will not change for the range of inventory policies that she is considering. Out-of-pocket costs for Parts Emporium to place an order with suppliers are estimated to be $30 per order for exhaust gaskets and $20 per order for drive belts. On the outbound side, the company can charge a delivery fee. Although most customers pick up their parts at Parts Emporium, some orders are delivered to customers. To provide this service, Parts Emporium contracts with a local company for a flat fee of $21.40 per order, which is added to the customer’s bill. McCaskey is unsure whether to increase the ordering costs for Parts Emporium to include delivery charges. Questions: 1. Provide brief answers (including the necessary explanations) to the following questions (no calculations are needed for these questions): i. Enumerate three major problems that Parts Emporium is facing. ii. McCaskey decided to randomly select a small sample of approximately 100 items and compile inventory and customer service characteristics to get a feel for the “total picture.” Can you suggest a better strategy? iii. Why limiting the study to two items only? iv. Should McCaskey increase the ordering costs for Parts Emporium to include delivery charges? v. What is the current inventory system? vi. What is the current level of service? vii. What is the proposed inventory system? Why? viii. How to convince the Executives of the company to adopt your recommendations? ix. How would the calculations for the two products be similar? How would they be different? x. What will be the next step for McCaskey if Block and Spriggs give her the backing needed to change the total inventory management system? 2. Complete the table below for the EG151 and show your detailed calculations in a separate file to be submitted as attachment (Excel, OM Explorer or POM doe Windows). Current Proposed % Change How much to order? When to order? Ordering plus holding cost per year: Estimated lost sales (in %): Estimated cost of lost sales per year: Total Cost per year: Most urgent action: The following questions are required only for the students who are submitting individually: 3. What is the role that IT can play in solving the problems faced by Parts Emporium? 4. How were internet sources helpful to you in solving this case?

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Question: Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Using t...

Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Using the listed​ actress/actor ages in various​ years, find the best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 27 years. Is the result within 5 years of the actual Best Actor​ winner, whose age was 45 ​years?

Best Actress: 27, 31, 29, 59, 34, 32, 44, 28, 65, 21, 45, 54

Best Actor: 45, 39, 40, 43, 52, 50, 59, 52, 41, 56, 44, 33

a. Find the equation of the regression line.

b. The best predicted age of the best actor winner given that the age of the best actress winner that is 27 years is ___years old.

A card is drawn from a standard deck of fifty-two cards which have been well-shuffled seven times. What is the probability that the card is:

(a) Either a face card (jack,queen, king) or a ten?

(b) Either a spade or a face card?

Note* Both the logic and mathematical calculation must be shown in the answers.

(07.01 MC)

The process of producing cholesterol medicine yields capsules with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 20 milligrams. The Consumer Watchdog Bureau tests a random sample of 80 tablets. The mean content of the active ingredient for this sample is 18.7 milligrams and the standard deviation is 5 milligrams. What is the approximate p-value for the appropriate test? (4 points)

6.

(07.04 MC)

Students at a local elementary school were randomly selected to participate in a reading fluency program. The program is designed to increase their reading fluency. A total of 17 students each took a pretest before the program and posttest after the program. The mean differences in the posttest and pretest is 11. The administration decided that all students in the school would participate in the program next school year. Let µA denote the mean score of the posttest and µB denote the mean score of the pretest for all students in the school. The 90 percent confidence interval estimate of the difference between the means for all students is (7, 15). What is an appropriate interpretation of the confidence interval? (4 points)

8.

(07.02 LC)

A student working on a report about mathematicians decides to find the 98% confidence interval for the difference in mean age at the time of math discovery for Greek mathematicians versus Egyptian mathematicians. The student finds the ages at the time of math discovery for members of both groups, which include all Greek and Egyptian mathematicians, and uses a calculator to determine the 98% confidence interval based on the t distribution. Why is this procedure not appropriate in this context? (4 points)

9.

(07.02 LC)

The manager of a computer repair shop wants to compare the mean number of motherboard repairs in a week for two repair techniques. Twenty-four technicians from the shop are selected randomly, and each technician is assigned randomly to one of the two techniques. After teaching 12 technicians one technique and 12 technicians the other technique, the manager records the number of motherboard repairs each technician performs in one week. Which of the following is the MOST appropriate inferential statistical test in this situation? (5 points)

10.

(07.02 LC)

Randall is conducting a test on bacteria on slices of cheese. He uses 10 slices of cheese to compare two strains of bacteria. He applies one strain to the left side of the cheese and one strain to the right side. He flips a coin to decide which strain goes on the right side of the cheese. The bacteria holes that appear on each side are counted and he records them in a table.

If Randall is to perform an appropriate t-test to determine if there is a difference in the mean number of holes per slice of cheese produced by the two strains, how many degrees of freedom should he use? (4 points)

11.

(07.05 MC)

In a study of the performance of a tires, the width of tires (in inches) and the life span (in months) for 14 tires were recorded. A regression line was a satisfactory description of the relationship between width of tire and tire life span. The results of the regression analysis are shown in the table.

Which of the following should be used to compute a 98% confidence interval for the slope of the regression line? (5 points)

12.

(07.05 LC)

The weight (in pounds) and the number of offspring of 23 randomly selected rabbits are compared. Which significance test should be used to determine whether a linear relationship exists between weight and number of offspring, provided the assumptions of the test are met? (4 points)

Suppose Avon and Nova stocks have volatilities of

50 %50%

and

23 %23%?,

?respectively, and they are perfectly negatively correlated. What portfolio of these two stocks has zero?risk?

The portfolio of these two stocks that has zero risk is

nothing?%

of Avon and

nothing?%

of Nova. ? (Round to two decimal? places.)

Dunbar Company had 1,000,000 shares of $1 par value common stock outstanding at January 1, 2015. On July 1, 2015, the company issued 100,000 additional shares of common stock. In addition, at December 31, 2015, 90,000 shares were issuable upon exercise of executive stock options which require a $40 cash payment upon exercise. The average market price during 2015 was $50.   

Dunbar Company also has two convertible securities. There are 10,000 convertible bonds with a face amount of $1,000, interest rate of 6% and convertible into 20 shares of common stock and 100,000 shares of 5%, $50 par value convertible preferred stock, convertible into 2 shares each.

During 2015, Dunbar Company’s net income was $24,000,000 and all preferred stock dividends were declared and paid. The company’s tax rate is 40%.

Instructions

Compute the diluted earnings per share for 2015.