A company manufactures two different types of gloves: a regular model and a catcher’s mitt.

The table below gives the basic information. Write the objective function, along with the constraints. All times are in hours.

1) Write a single function CalcArea( ) that has no input/output arguments. Inside the function, you will first print a “menu” listing 2 items: “rectangle”, “circle”.  It prompts the user to choose an option, and then asks the user to enter the required parameters for calculating the area (i.e., the width and length of a rectangle, the radius of a circle) and then prints its area.  The script simply prints an error message for an incorrect option.  

Here are two examples of running it:

>> CalcArea

Menu

1. Rectangle

2. Circle

Please choose one:2

Enter the radius of the circle: 4.1

The area is 52.81.

>> CalcArea

Menu

1. Rectangle
2. Circle

Please choose one: 1

Enter the length: 4

Enter the width: 6

The area is 24.00.

A professor has a class with four recitation sections. Each section has 16 students (rare, but there are exactly the same number in each class...how convenient for our purposes, yes?). At first glance, the professor has no reason to assume that these exam scores from the first test would not be independent and normally distributed with equal variance. However, the question is whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test.

First, run an ANOVA with this data and fill in the summary table. (Report P-values accurate to 4 decimal places and all other values accurate to 3 decimal places.

To follow-up, the professor decides to use the Tukey-Kramer method to test all possible pairwise contrasts.

What is the Q critical value for the Tukey-Kramer critical range (alpha=0.01)?
Use the website link in your notes (http://davidmlane.com/hyperstat/sr_table.html) to locate the Q critical value to 4 decimal places.
Q =

Using the critical value above, compute the critical range and then determine which pairwise comparisons are statistically significant?

• group 1 vs. group 2
• group 1 vs. group 3
• group 1 vs. group 4
• group 2 vs. group 3
• group 2 vs. group 4
• group 3 vs. group 4
• none of the groups are statistically significantly different

Assuming that the population is normally​ distributed, construct a 99% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

SAMPLE A: 1 1 4 4 5 5 8 8

SAMPLE B: 1 2 3 4 5 6 7 8

1.Construct a 99% confidence interval for the population mean for sample A. ( type integers or decimals rounded to two decimal places)

2. Construct a 99% confidence interval for the population mean for sample B.  ( type integers or decimals rounded to two decimal places)

3. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

a. The samples produce different confidence intervals because their standard deviations are different

b.The samples produce different confidence intervals because their sample sizes are different

c.The samples produce different confidence intervals because their critical values are different

d. The samples produce different confidence intervals because their medians are different

Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism, which he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results:

At the 0.05 Significance level, can he conclude that the number of absences has declined?

a. State the decision rule for 0.02 significance level: H₀ : μ_d ≤ 0; H₁ : μ_d > 0. (3 Decimal places)

Reject H₀ if t > _________.

b. Compute the value of the test statistic. (3 decimal places)

c. ESTIMATE the P-Value (4 decimal places)

C++ !

Create a Stash class specifically for storing Rect objects and call it RectStash. Add a default constructor and a destructor to correctly initialize your RectStash class. Then write a program that will read several lines as input. Each line will contain 4 floats defining a 2D rectangle in the Rect format described above. Read the rectangles adding them to a RectStash object. Stop reading rectangles when your program loads 4 negative float values. After this point you will start reading a series of 2D points, and for each 2D point you will print the classification of each point in respect to all previously read rectangles. The classification should print "in" or "out" according to its result. Stop your program when you read vector (-99,-99).

Everything should be contained in one file. You may not assume the existance of any header files in your working directory.

Sample Input:

-5 -5 2.5 2.5
5 8 2 2
-1 -1 -1 -1
0 0
-4 -6
6 9
-99 -99

result:

out out
in out
out out

First consider the following probability distribution for the total number of devices that connect to a home router.

X             p(x)

1             6%

2             4%         

3             2%

4             3%

5             4%

6             4%         

7             4%

8             5%

9             8%

10           10%

11           9%

12           8%

13           8%

14           6%

15           5%

16           4%

17           3%

18           3%

19           2%

20           2%

• Generate plots of the PDF and CDF for this distribution.
  • • Calculate the following o The expectation and the variance of the number of devices.
  • o The probability that a customer has 10 or fewer devices connecting.
  • o The probability that a customer has 14 or more devices connecting.
  • o The 50th percentile of the distribution.
  • • Now assume that the amount of data transferred per day is normally distributed with a mean of 15 GB and a standard deviation of 5 GB. Assume the data transferred each day is independent of other days. Calculate the following o The probability a customer transfers more than 18 GB in a day.
  • o The probability a customer transfers more than 18 GB for 3 days in a row.
  • o The 90th percentile of the daily transfer amount.

According to Michael Porter, the primary activities in a value chain include all except:

1) Sourcing & Procurement

2) Inbound Logistics

3) Operationss

4) Financial Management

5) Outbound Logistics