1. When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ.

Method 1: Use the Student's t distribution with d.f. = n − 1.
This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.

Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution.
This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution.

Consider a random sample of size n = 36, with sample mean x = 45.1 and sample standard deviation s = 6.0.

(a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(b) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(d) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(e) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

2. The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.)

(c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.)

Shown below is the activity for one of the products of Lawrence Creations:

January 1 balance, 80 units @ $50

Purchases:

January 19: 40 units @ $51

January 22: 30 units @ $52

January 29: 40 units @ $54

Sales:

January 13: 30 units @ $80

January 23: 50 units @ $80

January 31: 45 units @ $82

Required: Lawrence Creations uses a Period Inventory System. Compute ending inventory as of January 31 and sales, cost of goods sold and gross profit for the month of January for each of the following inventory cost flow assumptions:

a. FIFO b. Weighted Average c. LIFO

2. Dataset B consists of the values {10,12,14,24,25,27,28,30,30,32,33,33,34,37,38,38,40,41,43,

44,44,46,47,49,56,58}.

(a) What is the median of Dataset B?

(b) To one decimal, what is the sample standard deviation of Dataset B? (Don’t calculate this out by hand.)

(c) Make a table of the frequency distribution (not the relative frequency distribution) of Dataset B, using the intervals 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. Be sure to appropriately label the table headings.

(d) Make a graph of the relative frequency distribution (not the frequency distribution) of Dataset B, using the intervals 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. Be sure to appropriately label the horizontal and vertical axes.

Please calculate the payback period, IRR, MIRR, NPV, and PI for the following two mutually exclusive projects. The required rate of return is 15% and the target payback is 4 years. Explain which project is preferable under each of the four capital budgeting methods mentioned above:

Table 1

Cash flows for two mutually exclusive projects

Please calculate the payback period, IRR, MIRR, NPV, and PI for the following two mutually exclusive projects. The required rate of return is 15% and the target payback is 4 years. Explain which project is preferable under each of the four capital budgeting methods mentioned above:

Table 1

Cash flows for two mutually exclusive projects

v

Consider the monthly time series shown in the table.

1. Use the method of least squares to fit the model E(Yt) = β0 + β1t to the data. Write the prediction equation.
2. Use the prediction equation to obtain forecasts for the next two months.
3. Find 95% forecast intervals for the next two months.

Consider the monthly time series shown in the table.

1. Use the method of least squares to fit the model E(Yt) = β0 + β1t to the data. Write the prediction equation.
2. Use the prediction equation to obtain forecasts for the next two months.
3. Find 95% forecast intervals for the next two months.

6. In MS-22, read pages “4-32 to page 4-61. Write 5 sentences comparing and contrasting drum plants and batch plants. What are the main differences and what are the advantages of each type of plant?

7. In MS-22, read pages 4-20 to 4-24 on asphalt plant emissions systems. What are the two types of Primary and Secondary collectors? What happens to the collected particulate matter collected in these systems?

8. In MS-22 read pages 4-28 to 4-32. If the aggregate dryer in the mix plant is not operating correctly, list two possible deficiencies that may be encountered with the mix?

Renin is an aspartyl protease that has a role in the regulation of blood pressure. The active site has two aspartyl residues, one acting as an acid (pK1 5.0) and the other acting as a base (pK2 of 4.0). If the enzyme activity is measured at pH 6.0, what fraction of the enzyme is expected to be ACTIVE

A. 1% B. 9.0% C. 50% D. 90% E. 95% F. 99%