Question

1.   Describe what type of data analysis would use linear correlation coefficients and line of best fits. Describe the benefits of comparing to a line of best fit. (10 points)

2. Raw data is found in the excel file titled “STA322 Week 3 Data – Tab Line of Best Fit.” Calculate the linear correlation coefficient of that data and describe what that information provides. Find the slope and y intercept and list the line of best fit. Take Microsoft Excel and graph this line of best fit, using the “trend” function. Determine how you will implement the results you received to improve the data, base it on a scenario for your career. (30 points)

3. Express the likelihood given as a probability between 0 and 1 for the following (20 points):

                a. The Weather Channel stated that we have a 75% chance of being hit by the hurricane.

                b. I have a 22% chance of winning the Sweepstakes.

                c. When playing Yahtzee, I can roll 1 die and I need a 4. What are my chances?

                d. The gender of the new baby being a girl.

4. A survey was taken at a K-6^th grade school. Do you have enough time at lunch? Given the table below, answer the following questions (20 points):

	Yes	No
Girls	35	124
Boys	100	62

               

If b represents the event of selecting a response from a boy, find P(Ђ).

Find the probability that the selected answer was made by a girl or was answered no.

If g represents the event of selecting a response from a girl, find P (ḡ).

Find the probability that the selected answer was made by a boy and answered yes.

5. Find the number of ways that 6 Discussion responses can be ordered by calculating 6! (5 points)

6. Find the number of ways that the 5 children can line up to go to recess by calculating 5! (5points)

Use Permutations or Combinations on the next 3 examples:

7. If you are allowed to use numbers 1 – 20 and need to choose the passcode of an exact 4 digit code, how many possibilities are there? (10 points)

8. If there are 25 students in the class and we need to select a President and Secretary for our meetings, how many possibilities are there? (10 points)

9. In playing a card game, I am dealt 6 cards, how many possibilities are there for my hand? (10 points)

Answer 1

1. The line of best fit is a good model when there is a strong positive or negative correlation between the dependent and independent variables. Generally, if the correlation is gretaer than 0.8 in magnitude, it indicates a strong correlation. The formula for correlation coefficient is

3. a 75% chance equals probability of 0.75

b. 0.22

c. In rolling a die, there are 6 possibilities, all of which are equally likely. As I need a 4, which is one out of those events, the probability is  

d. Gender can be boy or girl. Both are equally likely. So probability is  

4. Given data can be further summarized as below

	Yes	No
Girls	35	124	159
Boys	100	62	162
	135	186	321

1. Probability of NOT selecting a response from a boy   

2. Total count of Girls or reponse No = 159 + 62 = 221. Probability

Note that word OR means adding the required cell values, and whichever are common should only be counted once. Like here value of 124 is common.

3.

4. Probability that answer made by a Boy and answered Yes  

Note that AND means common intersection value. So it is the cell of Boys who answered yes.

5. No of ways to order 6 discussion responses

6. No of ways to line up 5 children

7. Each digit, except the first, can have all of the 10 digits. The first digit has only 9 options, 0 cannot be there. So by fundamental principle of counting, No of ways

8. We need to select 2 people from a group of 25. No of ways  

9. No of possibilities for my hand = No of ways to select 6 from 52 cards