Chapter 10
6. Test H₀: 8 versus H_A: > 8, given = 0.01, n = 25, = 8.13 and s = 0.3. Assume the sample is selected from a normally distributed population.

7. Test H₀: π = 0.25 versus H_A: π 0.25 with p = 0.33 and n = 100 at alpha = 0.05 and 0.10.

8. Test at α = 0.01 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 285 favor the system?

9. Test whether the sample evidence indicates that the average time an employee stays with a company in their current positions is less than 3 years when a random sample of 64 employees yielded a mean of 2.76 years and s = 0.8. Use = 0.01. Assume normal distribution.

Consider a 1550 nm laser diode with a rise time of 0.8 ns, spectral half-width of 6 nm, that launches 2 mW optical power into a 60 km long single-mode fiber with an attenuation of 0.3 dB/km. The intramodal dispersion is 3 ps/nm.km. An InGaAs APD with a -32 dBm sensitivity is used at 2.5 Gb/s (NRZ coding). A short optical jumper cable at each end of the cable with a loss of 3 dB is used to connect the fiber to the equipment rack. In addition, the connector loss at each joint between the jumper and fiber cable and jumper and equipment rack is 1 dB each. Determine the temporal response of the system components and calculate the maximum transmission rate. Discuss if the system is bandwidth limited.

1. As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of 240 units per eight-hour day. Task times and precedence relationships are as follows:

1. Draw the precedence diagram.
2. Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time.
3. Determine the minimum number of stations needed.
4. Assign tasks to workstations on the basis of most following tasks. Use longest processing time as a tiebreaker. If ties still exist, assume indifference in choice.
5. Compute the percentage of idle time for the assignment in part d.

Stock A is expected to produce the following returns given various states of the economy:
Table 1 - Stock A

Table 2 - Stock B and Stock C

1) What is the expected return of stock A?
2) What is the standard deviation of the expected return of stock A?
3) If an investor is considering combine stock A with another stock to build a two-stock portfolio, which one of the two (Stock B or Stock C) is a better choice with the given information in Table 2 and why?

Please show all the work.

If the quantity of coffee-drink produced per hour (regular day hour) at a company and the costs of production are given as shown in the table below, do you think that Starbucks is experiencing economies of scale? Why or why not?   

If the price of a coffee-drink is $6, what is the quantity that maximize company profit?

Under the assumptions of Modigliani and Miller’s original paper, a firm’s stock price will be maximized at 100% (debt, equity) . Signaling theory implies that a firm with extremely favorable prospects will be more likely to issue (stock, debt) to fund any new projects. When a firm announces a new stock offering, the price of its stock will usually (increase, decrease)   . When information is (asymetric, symetric)   , managers have more information about a firm’s prospects than investors do.

Drugal Brewing Co. currently has no debt in its capital structure, but it is considering using some debt and reducing its outstanding equity. The firm’s unlevered beta is 1.20, and its cost of equity is 11.40%. Because the firm has no debt in its capital structure, its weighted average cost of capital (WACC) also equals 11.40%. The risk-free rate of interest (rRFrRF) is 3%, and the market risk premium (RP) is 7%. Drugal Brewing Co.’s marginal tax rate is 35%.

Drugal Brewing Co. is examining how different levels of debt will affect its costs of debt and equity, as well as its WACC. The firm has collected the financial information that follows to analyze its weighted average cost of capital (WACC). Complete the following table.

Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use = .05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A Consultant B   = 16   = 10   = 6.82   = 6.25   = 0.7   = 0.8 State the null and alternative hypotheses. H0: 1 - 2 Ha: 1 - 2 Compute the value of the test statistic (to 2 decimals). What is the p-value? Use z-table. The p-value is What is your conclusion?

Two students, Jim and Kim, are planning all-nighter to prepare for their interviews the following morning. Between them, they have only one set of materials in the following 5 subjects: OM, PS, MKT, FIN, ACC. Based on their previous experience, they estimate that they will need the following amount of time (in hours) with each set of materials.

They agree that Kim will get the opportunity to see each set of notes before Jim. Assume that they start their study at 8:00 pm. Determine the exact times that each will begin and end by studying each subject in order to maximize combined sleep they can get before the interview. Give the rule used.

1. Let X and Y equal the number of milligrams of tar in filtered and nonfiltered cigarettes, respectively. Assume that ?~?(?_?, ?²) and ?~?(?_?, ?²). We shall test the null hypothesis ?₀: ?_? = ?_? against the alternative hypothesis ?_?: ?_? < ?_? using independent random samples of sizes n = 9 and m = 11 observations from X and Y, respectively.
   1. Define the test statistic for testing the above hypothesis, and the rejection region that is associated with an ? = 0.01 significance level. Sketch a figure illustrating this rejection region.
   2. Given the n = 9 observations on X: 0.9, 1.1, 0.1, 0.7, 0.4, 0.9, 0.8, 1.0, 0.4; and the m = 11 observations on Y: 1.5, 0.9, 1.6, 0.5, 1.4, 1.9, 1.0, 1.2, 1.3, 1.6, 2.1, calculate the value of the test statistic and clearly state your conclusion. Locate the value of the test statistic on your figure.
   3. What is the p-value of this test?

15. A company’s top brand shows the following data of its unit selling price and its corresponding sales amount:

1) Find a simple linear regression model with X = unit selling price and Y = sales amount.

2) If the company lowers its selling price to $10, what would be the expected sales amount?

3) Based on the regression model you find, estimate the change of sales amount (increase or decrease) according to one dollar increase of product price.

4) As you know, the sales amount is affected by many different variables such as price, advertising, quality, product design, etc. what would you think how much the product price variable has an impact on sales in terms of percentage?