This information is for problems 7 – 14:
Two economics professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
                                                Mean Grade                      Standard Deviation
Professor Welker            83.6                                                        21.6
Professor Ackerman       79.7                                                        12.0
At the 0.01 level of significance, what is your conclusion?

This information is for problems 7 – 14:
Two economics professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
                                                Mean Grade                      Standard Deviation
Professor Welker            83.6                                                        21.6
Professor Ackerman       79.7                                                        12.0
At the 0.05 level of significance, what is your conclusion?

7. Identify two factors that affect the lifetime of pollutants in the atmosphere, and explain how these two factors affect pollutant lifetime. (SHORT ESSAY)

Two candidates are competing in a majority rule election with 7 voters. The possible policies are ordered on a number line and creatively labeled {1, 2, 3, 4, 5, 6, 7}. Each policy is the favorite of one voter, and each voter has single peaked preferences. The candidates, L and R, announce policies, and whomever gets the most votes wins and implements the policy she announced. (Each voter votes for whichever candidate they strictly prefer. If a voter is indifferent, she allocates exactly half a vote to each candidate. If the candidates tie, they flip a coin, and the winner of the coin toss wins the election and implements the policy she announced.) Unlike the Downsian model, the candidates also have single peaked policy preferences. Candidate L’s favorite policy is 2. Candidate R’s favorite policy is 6. (Politics is pretty polarized these days.) In addition, the winning candidate obtains 10 jollies from winning the election.

So:

• if L wins with a policy of k in {1,2,3,4,5,6,7}, then L obtains −|2 − k| + 10 jollies, and R obtains −|6 − k| jollies.

• If R wins with a policy of j in {1,2,3,4,5,6,7}, then candidate L obtains −|2 − j| jollies, and R obtains −|6 − j| + 10 jollies.

(a) If L announces a policy of 4, what is R’s best response?

(b) Is it a Nash equilibrium of this game for each candidate to announce 4?

(c) Is it a Nash equilibrium for each candidate to announce her ideal point?

(d) Does your answers change if the candidates each obtain 2 jollies from winning the election?

7. Let m be a fixed positive integer.

(a) Prove that no two among the integers 0, 1, 2, . . . , m − 1 are congruent to each other modulo m.

(b) Prove that every integer is congruent modulo m to one of 0, 1, 2, . . . , m − 1.

There are at least 10 errors in the following C program. For each error you can find you should list the location of the error, describe what the error is, and state how the error can be fixed (write updated code for that line if necessary). Each error you find is worth 1.5 marks. Note that missing brackets, braces, etc count as only one error, even though the missing brackets may occur at two places.

The program is supposed to perform the following task: Read a list of names and heights from a file called “heights.txt”. Each line of the file contains a single name (one word, 50 chars max) and an integer value representing that person’s height in cm. These names and heights should be stored in two arrays, with a maximum size of 1000. Once this is done, the user should be asked to enter a minimum and maximum height (in cm), and the program should display all people whose heights fall between those values (inclusive). If a zero is entered for either criteria, then that criteria is not checked. For example, if the user enters 0 for the maximum height, then there is no maximum value and all people above the minimum height will be listed. If both values are zero then all people will be listed. The names and heights should be displayed one per line, with the name first followed by a colon, then the height in cm. At the end of the program the total number of people matching the search criteria should be displayed as well.

1 #include <stdio.h>
2
3 int main ( void ){
4
5    int heights[1000], i, n = 0, total = 0, min, max ;
6       char names[50][1000] ;   
7 file *fp ;
8
9       fp = fopen ( "heights.txt", "w" ) ;
10       if ( fp == NULL ){
11          printf ( "Cannot open heights.txt for reading\n" ) ;
12          exit ( -1 ) ;
13       }
14       while (n<1000 && scanf("%c %d",names[n],&heights[n])!=EOF){
15          n++ ;   
16       }
17
18       printf ( "Enter minimum height to display: " ) ;
19 scanf ( "%d", &min ) ;
20       printf ( "Enter maximm height to display: " ) ;
21       scanf ( "%d", &max ) ;
22
23 for ( i = 0 , i <= n , i++ ){
24 if ((heights[i]>=min || min==0)|| (heights[i]<=max || max==0)){
25 // display the person and height
26 printf ( "%c: %dcm\n", names[i][50], heights[i] ) ;
27   }
28 }
29 printf ( "Total matches: %d\n", total ) ;
30 return (0);
31 }

Suppose a random sample of size 50 is selected from a population with

σ = 8.

Find the value of the standard error of the mean in each of the following cases. (Use the finite population correction factor if appropriate. Round your answers to two decimal places.)

(a)

The population size is infinite.

(b)

The population size is

N = 50,000.

(c)

The population size is

N = 5,000.

(d)

The population size is

N = 500.

Suppose that the annual demand will be 10000 units. The company operates 250 days/year, with two 8-hour shifts a day. Management believes that a capacity cushion of 15% is the best. Average lot site is 50 units and the standard processing time is 0.5 hours. Each lot requires 0.2 hours standard set up time. How many production line would be needed to compensate the demand?(15pts)

You may need to use the appropriate appendix table or technology to answer this question.

A simple random sample of 50 items from a population with

σ = 8

resulted in a sample mean of 38. (Round your answers to two decimal places.)

(a)

Provide a 90% confidence interval for the population mean.

to

(b)

Provide a 95% confidence interval for the population mean.

to

(c)

Provide a 99% confidence interval for the population mean.

to

SAP Co. uses a periodic inventory system. It records show the following for the month of February:

Date Units UnitPrice Total Cost

2/1 40 $20.00 $800

2/15 Purchases 130 22.00 2,860

2/24 Purchases 110 23.50 2,585

Totals   280 $6,245

2/20 Sales 100 47.00

2/27 Sales 130 47.00

Given the information above, please calculate COGS,Ending Inventory, and Gross Profit under each of the following methods. (Please explain)

1) FIFO:

2) LIFO:

3) Average Cost:

I know this is a long problem but I couldn't break it up because you need all the information. But it is only counted as one question on my homework.

Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wasted per person in traffic delays. A random sample of eight cities showed the following data.

Verify that Σx = 156, Σx² = 3918, Σy = 240, Σy² = 9308, and Σxy = 6011.

Compute r._____________?

The data in part (a) represent average annual hours lost per person and average annual gallons of fuel wasted per person in traffic delays. Suppose that instead of using average data for different cities, you selected one person at random from each city and measured the annual number of hours lost x for that person and the annual gallons of fuel wasted y for the same person.

(b) Compute x and y for both sets of data pairs and compare the averages.

Compute the sample standard deviations s_x and s_y for both sets of data pairs and compare the standard deviations.

Verify that Σx = 172, Σx² = 5026, Σy = 268, Σy² = 13,516, and Σxy = 7858.

Compute r.__________?

List some reasons why you think hours lost per individual and fuel wasted per individual might vary more than the same quantities averaged over all the people in a city.