1. Fusible interlinings are being used with increasing frequency to support outer fabrics and improve the shape and drape of various pieces of clothing. The article “Compatibility of Outer and Fusible Interlining Fabrics in Tailored Garments” (Textile Res. J., 1997: 137-142) gave the accompanying data on extensibility (%) at 100 gm/cm for both high-quality fabric (H) and poor-quality fabric (P) specimens:

H: 1.2, .9, .7 ,1.0, 1.7, 1.7, 1.1, .9, 1.7, 1.9 ,1.3, 2.1 ,1.6, 1.8, 1.4, 1.3 ,1.9 ,1.6, .8 2.0 ,1.7, 1.6, 2.3, 2.0

P: 1.6, 1.5, 1.1, 2.1, 1.5, 1.3, 1.0, 2.6

(a) Assuming the samples came from approximate normal populations, run a test at the ?=0.05 significance level to determine whether the true average extensibility differs for the two types of fabrics. Be sure to follow the directions given at the top of the assignment.

(b) Construct a 95% confidence interval for ??−??, the difference between the average extensibility of the two fabrics. Explain how you could draw your conclusion in part (a) by using this confidence interval.

a) Use XLSTAT to compute a 95% confidence interval for the average percent audited of districts with an average adjusted gross income of $35,000. Interpret the interval in the context of the application.

b) Use XLSTAT to compute a 95% prediction interval for the percent audited of an individual district with an average adjusted gross income of $35,000. Interpret the interval in the context of the application.

c) Use the regression output in XLSTAT to calculate the coefficient of determination, r2r2 from the sum of squares due to regression (SSR) and the total sum of squares (SST). Interpret your calculated value of r2r2 in the context of the application.

a) Use XLSTAT to compute a 95% confidence interval for the average percent audited of districts with an average adjusted gross income of $35,000. Interpret the interval in the context of the application.

b) Use XLSTAT to compute a 95% prediction interval for the percent audited of an individual district with an average adjusted gross income of $35,000. Interpret the interval in the context of the application.

c) Use the regression output in XLSTAT to calculate the coefficient of determination, r2r2 from the sum of squares due to regression (SSR) and the total sum of squares (SST). Interpret your calculated value of r2r2 in the context of the application.

1. Lucy always uses an alpha level of 0.01 (two-tailed). Charlie always uses an alpha level of 0.05 (two-tailed). Which researcher is more likely to make a Type I Error. Lucy or charlie?

2. A researcher is interested in whether blood pressure decreases among adults who eat dark chocolate. The mean systolic blood pressure of the population is 135 with a standard deviation of 15. She tests a sample of 100 adults who eat dark chocolate and finds their mean systolic blood pressure to be 120. What is the null hypothesis?

   		μ = 135
   		μ ≠ 135
   		μ  > 135
   		μ ≥ 135

3. According to Cohen's d conventions, which of the following would be considered to be a medium effect size?

   		-0.55
   		0.81
   		-0.98
   		0.17

4. With α = 0.05, what is the critical t value for a one-tailed test with n = 15?

   		t = 1.761
   		t = 1.753
   		t = 2.145
   		t = 2.131

5. What z-score values form the boundaries for the middle 68% of a normal distribution?

   		z = +0.2 and z = - 0.2
   		z = +0.4 and z = - 0.4
   		z = +0.8 and z = - 0.8
   		z = +1.0 and z = - 1.0

1. An army recruit is on a training exercise and instructed to walk due west for 8 km,
then in a north-easterly direction for 4 mi, and finally due north for 15,840 ft. How far
will he be from where he started?
2. A tittle turtle is placed at the origin of an xy grid drawn on a large sheet of paper.
Each grid box is 1.0 cm by 1.0 cm. The turtle walks around for a while and finally
ends up at point (24, 10), that is, 24 boxes along the x-axis, and 10 boxes along the
y-axis. Determine the displacement of the turtle from the origin at the point.
3. A bug starts at point A, crawls 8.0 cm east, then 5.0 cm south, 3.0 cm west, and 4.0
cm north to point B. (a) How far north and east is B from A? (b) Find the
displacement from A to B both graphically and algebraically.
4. A woman jogs 4.2 km east and then 2.9 km south at a speed of 8.0 km/h. How much
time would she have saved if she had jogged directly to her destination?

34. Consider a firm producing and selling joint products produced in variable proportions in two competitive markets. For a given level of TC (or a level TR), the profit-maximizing combination of QA and QB requires _______, where PA = price of A, PB = price of B, CA = cost of A and CB = cost of B. MC of A and B can be used for CA and CB.

A. P_A/C_A =P_B/C_B B. P_A/C_B =P_B/C_A C. P_A/C_A -P_B/C_B =1. D. P_A/C_A +P_B/C_B = 1.0 E. None of the above.

35. Consider a firm producing and selling joint products produced in variable proportions in non-competitive markets. For a given level of TC (or a level TR), the profit-maximizing combination of QA and QB requires _______, where PA = price of A, PB = price of B, CA = cost of A and CB = cost of B. MC of A and B can be used for CA and CB.

A. P_A/C_A =P_B/C_B B. P_A/C_B =P_B/C_A C. P_A/C_A -P_B/C_B =1. D. P_A/C_A +P_B/C_B = 1.0 E. None of the above.

1. Smith’s HVAC is considering making a change to its capital structure in hopes of increasing its value. The company's capital structure consists of debt and common stock. In order to estimate the cost of debt, the company has produced the following table:

The company uses the CAPM to estimate its cost of common equity, r_s. The risk-free rate is 5% and the market risk premium is 6%. Smith’s estimates that if it had no debt its beta would be 1.0. (Its "unlevered beta," b_U, equals 1.0.) The company's tax rate, T, is 40%.

On the basis of this information, what is Smith's optimal capital structure, and what is the firm's cost of capital at this optimal capital structure?

Aaron Athletics is trying to determine its optimal capital structure. The company’s capital structure consists of debt and common stock. In order to estimate the cost of debt, the company has produced the following table:

Debt-to-total-             Equity-to-total-              Debt-to-equity           Bond       B-T cost

assets ratio (w_d)          assets ratio (w_c)               ratio (D/E)                rating      of debt

0.10                            0.90                      0.10/0.90 = 0.11         AA      7.0%

0.20                            0.80                      0.20/0.80 = 0.25           A        7.2

0.30                            0.70                      0.30/0.70 = 0.43           A        8.0

0.40                            0.60                      0.40/0.60 = 0.67          BB       8.8

0.50                            0.50                      0.50/0.50 = 1.00           B        9.6

The company’s tax rate, T, is 40 percent.

The company uses the CAPM to estimate its cost of common equity, k_s. The risk-free rate is 5 percent and the market risk premium is 6 percent. Aaron estimates that if it had no debt its beta would be 1.0. (Its “unlevered beta,” b_U, equals 1.0.)

On the basis of this information, what is the firm’s weighted average cost of capital (WACC) at its optimal capital structure?

Q1. From a reputed store’s record it was found that weight of sugar bags sold by it is normally distributed

       with mean 1.0 lb. and standard deviation of 40 g.

a. What is the probability/chances/likelihood that

i. a bag selected randomly will be lighter than 400 g (0.0901)

ii. a bag selected randomly will be heavier than 600 g (0.00013)

         iii. the weight will be more than 463.5 g. if a customer bought one bag,? (0.4013)

       b What proportion of customers are expected to buy heavier than 470 g,

           if one customer can buy one bag? (0.3409)

       c. How many bags are expected to be heavier than 470 g,

          if it has a stock of 1000 bags in the store? (341 bags)

       d. What proportion of bags will be heavier than 1.0 lb.? (0.5)

       e. A random sample of 64 bags was selected.

         i. mean weight of the sample will be more than 461.8 g.? (0.0505)

         ii. the mean weight will between 443.8 g. to 463.4 g.(0.95)

       f. From what weight

           i. 25% bags will be heavier? (480.6 g.)    ii. 25% bags will be lighter? (426.6 g.)

How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about 1. The National Institution of Standards and Technology provides exact data on properties of materials. Here are 11 measurements of the heat conductivity of a particular type of glass.

1.11 1.05 1.12 1.07 1.13 1.07 1.08 1.15 1.17 1.18 1.13

(a) We can consider this an SRS of all specimens of glass of this type. Make a stemplot. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

Stems Leaves

1.0 1.0 1.1 1.1

Is there any sign of major deviation from Normality?

The stemplot shows that the data are not skewed and have no outliers.

The stemplot shows that the data is skewed to the left with one outlier.

The stemplot shows that the data is skewed to the right with one outlier.

(b) Give a 80% confidence interval for the mean conductivity. (Use 3 decimal places.)

(__________ , __________)