R-9.6 Explain where the induction proof for showing that deterministic selection runs in O(n) time would fail if we formed groups of size 3 instead of groups of size 5.

Using the following data set:

Observation   Brand   Price ($)   Megapixels   Weight (oz.)   Score
1   Canon   330   10   7   66
2   Canon   200   12   5   66
3   Canon   300   12   7   65
4   Canon   200   10   6   62
5   Canon   180   12   5   62
6   Canon   200   12   7   61
7   Canon   200   14   5   60
8   Canon   130   10   7   60
9   Canon   130   12   5   59
10   Canon   110   16   5   55
11   Canon   90   14   5   52
12   Canon   100   10   6   51
13   Canon   90   12   7   46
14   Nikon   270   16   5   65
15   Nikon   300   16   7   63
16   Nikon   200   14   6   61
17   Nikon   400   14   7   59
18   Nikon   120   14   5   57
19   Nikon   170   16   6   56
20   Nikon   150   12   5   56
21   Nikon   230   14   6   55
22   Nikon   180   12   6   53
23   Nikon   130   12   6   53
24   Nikon   80   12   7   52
25   Nikon   80   14   7   50
26   Nikon   100   12   4   46
27   Nikon   110   12   5   45
28   Nikon   130   14   4   42

10. Test whether price and score are correlated, using level of significance ? = 0.01

11. Test for the significance of the relationship between price and score, using level of significance ? = 0.01.

12. Construct and interpret a 90% confidence interval for the slope of the population regression line between price and score.

1. Find x and y so that the ordered data set has a mean of 42 and a median of 35, hence compute the harmonic mean and geometric mean of the data sample.

       17, 22, 26, 29, 34, x, 42, 67, 70, y                                                         

2. The lengths, in centimeters, of 18 snakes are given below. Draw an ordered stem-and-leaf diagram for the data.                                                                                                                                    

24, 62, 20, 65, 27, 67, 69, 32, 40, 53, 55, 47, 33, 45, 55, 56, 49, 58

3. Costs of production have been monitored for some time within a company and the following data found:

1. Calculate the correlation coefficient.                                                                        
2. Calculate the coefficient of determination and explain its significance for the company.                                                                                                                                                   

4. Using the following frequency distribution table;

Find

1. The mean                                                                                                       
2. Median                                                                                                           
3. Standard deviation                                                                                         
4. Coefficient of skewness and comment                                                          

5. A single fair die is tossed. What is the probability that the score is a prime number?                
6. The following data represents the comparison made between the price of a consumer product and the corresponding demand.

      Determine the linear regression equation of the form y= a+bx that relates price (x) and demand (y).                                                                                                                                                                        

7. An integer is randomly selected between 1 and 50, inclusively. Find the probability that the number is not divisible by 7.                                                                                                                              

There are three arrangements of the word DAD, namely DAD, ADD, and DDA. How many arrangements are there of the word PROBABILITY?            

Your Toronto Maple Leafs won 30 of 82 games last season (i.e., the 2014-2015 season), giving them a winning percentage of 37%. If we assume this means the probability of the Leafs winning any given game is 0.37, then we can predict how they would have done in a playoff series.

Answer the following questions to determine the probability that the Leafs would have won a best of 7playoff series (i.e., won 4 games) had they made the playoffs last season.

a. Rephrase this question in terms of sequences of 0s and 1s. What is the shortest length of a sequence? What is the longest length of a sequence?

b. Calculate the number of sequences which correspond to the Leafs winning the series. (Note that the answer is not C(7, 4).)

c. Calculate the number of sequences as they relate to this problem. (Note that the answer is not 27 as not all series would last 7 games.)

d. Calculate the probability that the Leafs would win the series.

e. What is your best guess for the probability that the Leafs will ever win the Stanley Cup again (the ultimate prize in the NHL)

A hare and a tortoise compete in a race over a straight course 1.10 km long. The tortoise crawls at a speed of 0.160 m/s toward the finish line. The hare runs at a speed of 7.50 m/s toward the finish line for 0.880 km and then stops to tease the slow-moving tortoise as the tortoise eventually passes by. The hare waits for a while after the tortoise passes and then runs toward the finish line again at 7.50 m/s. Both the hare and the tortoise cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds. (a) How far is the tortoise from the finish line when the hare resumes the race?

A man of mass 80 kg runs up a flight of stairs 20 m high in 10 s. (a) how much power is used to lift the man? (b) If the man’s body is 25% efficient, how much power does he expend? (c) This man consumes approximately 1.05 × 107 J (2500 food calories) of energy per day while maintaining a constant weight. What is the average power he produces over a day? (d) Compare this with his power production when he runs up the stairs.

Answer is: a) 1.6 kW; (b) 6.3 kW; (c) 122 W; (d) 1.9% of power produced running up stairs

A publisher reports that 48%48% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually under the reported percentage. A random sample of 110110 found that 40%40% of the readers owned a personal computer. Is there sufficient evidence at the 0.050.05 level to support the executive's claim?

Step 1 of 7:

State the null and alternative hypotheses.

Step 2 of 7:

Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 7:

Specify if the test is one-tailed or two-tailed

Step 4 of 7:

Determine the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 7:

Identify the value of the level of significance.

A cloth manufacturer finds that 8% of their production are defective. What is the probability that a batchof 10 willcontain (a) more than two defectives? (b) Less than seven defectives? (c) Exactly eight defectives.

Here is a table showing all

52

cards in a standard deck.

A five-card hand is dealt at random from a standard deck. (A five-card hand is any set of five different cards, chosen without replacement.)

What is the probability that the hand contains exactly two red cards?

Round your answer to the nearest hundredth.

1. Given the declaration

            char table[7][9];

                which of the following stores the character 'B' into the fifth row and second column of the array?

            A) table[5] = 'B';

            B)   table[2][5] = 'B';

            C)   table[5][2] = 'B';

            D) table[1][4] = 'B';

            E)   table[4][1] = 'B';

2. This program fragment is intended to zero out a two-dimensional array:

int arr[10][20];

            int i, j;

            for (i = 0; i < 10; i++)

                  for (j = 0; j < 20; j++)

                      // Statement is missing here

                What is the missing statement?

            A) arr[j+1][i+1] = 0;

            B)   arr[i-1][j-1] = 0;

            C)   arr[i+1][j+1] = 0;

            D) arr[i][j] = 0;

            E)   arr[j][i] = 0;

3. Given this nested For loops

  for (i = 0; i < M; i++)

                  for (j = 0; j < N; j++)

                      cout << arr[i][j];

                what is the appropriate declaration for arr?

            A) int arr[M+N];

            B)   int arr[M+1][N+1];

            C)   int arr[M][N];

            D) int arr[N][M];

            E)   int arr[N+1][M+1];

4. Given the declarations

            float alpha[5][50];

            float sum = 0.0;

                which one computes the sum of the elements in row 2 of alpha?

            A) for (i = 0; i < 50; i++)

                           sum = sum + alpha[2][i];

            B)   for (i = 0; i < 5; i++)

                           sum = sum + alpha[2][i];

            C)   for (i = 0; i < 50; i++)

                           sum = sum + alpha[i][2];

            D) for (i = 0; i < 5; i++)

                           sum = sum + alpha[i][2];

5. Look at the following array definition.

int numberArray[9][11];

Write a statement that assigns 130 to the first column of the second row of this array.

6. Write a statement which will assign 18 to the last column of the last row of this array.

Values is a two-dimensional array of floats that include 10 rows and 20 columns. Write a

code that sums all the elements in the array and stores the sum in the variable named total.