To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in the table below.

Find the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)

t= P-value=

State the conclusion in the problem context.

We fail to reject H₀. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed.

We fail to reject H₀. The data provide convincing evidence that swimming in guar syrup changes mean swimming speed.    

We reject H₀. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed.

We reject H₀. The data provide convincing evidence that swimming in guar syrup changes mean swimming speed.

1. SWS Company currently purchases 6,000,000 units per year of a particular part from WDS Industries. The current contract sets the price at $1.00 per unit and allows one reject for each 10,000 rings purchased. SWS inspects all incoming units at a cost of $250,000 per year. The inspection station correctly identifies 100% of the acceptable units and 75% of the units that do not meet SWS’s quality criteria. Unacceptable units that pass through the inspection station lead to a shutdown in SWS’s production process during the next step. Each shutdown costs SWS an estimated $15,600 in incremental out-of-pocket costs. SWS would like to increase the incoming quality from WDS Industries to one reject per 1,000,000 units. WDS has agreed to this change but insists on a price of $1.40 per ring.

A. Under the conditions stated above, and assuming no other changes, should SWS change to the higher quality requirement? Be sure to state explicitly the criteria on which you base your decision.

B. Now assume that if SWS chooses the higher quality requirement it will eliminate the inspection station and all associated costs. Under these conditions, should SWS change to the higher quality requirement? Be sure to state explicitly the criteria on which you base your decision.

C. Now assume that, if the company changes to the higher quality requirement, the cost of a shutdown in SWS’s production process also changes. What change in the cost per shutdown would make SWS indifferent between the two quality requirements? Assume that SWS eliminates the inspection station if it chooses the higher quality requirement. Note that the cost of a shutdown does not change unless SWS changes to the higher quality requirement.

Castle, Inc., has no debt outstanding and a total market value of $180,000. Earnings before interest and taxes, EBIT, are projected to be $25,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 10 percent higher. If there is a recession, then EBIT will be 20 percent lower. The firm is considering a $60,000 debt issue with an interest rate of 5 percent. The proceeds will be used to repurchase shares of stock. There are currently 6,000 shares outstanding. Ignore taxes for this problem.

A-1 Calculate earnings per share, EPS, under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations and round your answers to 2 decimal places e.g., 32.16.)

A-2 Calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to the nearest whole number e.g., 32.)

B-1 Calculate earnings per share (EPS) under each of the three economic scenarios assuming the company goes through capitalization. (Do not round intermediate calculations and round your answers to 2 decimal places e.g., 32.16.)

B-2 Given the recapitalization, calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to the nearest whole number e.g., 32.)

Castle, Inc., has no debt outstanding and a total market value of $250,000. Earnings before interest and taxes, EBIT, are projected to be $40,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 20 percent higher. If there is a recession, then EBIT will be 20 percent lower. The firm is considering a debt issue of $105,000 with an interest rate of 4 percent. The proceeds will be used to repurchase shares of stock. There are currently 10,000 shares outstanding. The firm has a tax rate 35 percent. Assume the stock price remains constant. a-1. Calculate earnings per share (EPS) under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) EPS Recession $ Normal $ Expansion $ a-2. Calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to the nearest whole number, e.g., 32.) Percentage changes in EPS Recession % Expansion % b-1. Calculate earnings per share (EPS) under each of the three economic scenarios assuming the company goes through with recapitalization. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) EPS Recession $ Normal $ Expansion $ b-2. Given the recapitalization, calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage changes in EPS Recession % Expansion %

Variable Costing Income Statement and Contribution Margin Analysis for a Service Company

The actual and planned data for Underwater University for the Fall term were as follows:

Registration, records, and marketing costs vary by the number of enrolled students, while instructional costs vary by the number of credit hours. Depreciation is a fixed cost.

a. Prepare a variable costing income statement showing the contribution margin and income from operations for the Fall term.

b. Prepare a contribution margin analysis report comparing planned with actual performance for the Fall term. If an amount is zero, enter "0".

Castle, Inc., has no debt outstanding and a total market value of $240,000. Earnings before interest and taxes, EBIT, are projected to be $26,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 18 percent higher. If there is a recession, then EBIT will be 20 percent lower. The firm is considering a debt issue of $150,000 with an interest rate of 8 percent. The proceeds will be used to repurchase shares of stock. There are currently 15,000 shares outstanding. Ignore taxes for this problem.

a-1. Calculate earnings per share, EPS, under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

a-2. Calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to the nearest whole number, e.g., 32.)

b-1. Calculate earnings per share (EPS) under each of the three economic scenarios assuming the company goes through with recapitalization. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

b-2. Given the recapitalization, calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)