Week8 finalexamlivelecture 2010december

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Latest Final Exam Lecture Math 221

Transcript of Week8 finalexamlivelecture 2010december

  • 1. Lecture for the Final ExamStatistics For Decision Making
    B Heard
    Not to be used, posted, etc. without my expressed permission.B Heard

2. Week 3 Quiz
Some Things to Remember
Not to be used, posted, etc. without my expressed permission.B Heard
3. This data shows the Lab Report scores of 8 selected students and the number of hours they spent preparing their Statistics Lab Report. 40 was the highest score the student could make.
(hours, scores),
(3,34), (2,30), (4,38), (4,40), (2,32), (3,33), (4,37), (5,39)
Not to be used, posted, etc. without my expressed permission.B Heard
4. Find the equation of the regression line for the given data.
What is the r2 for the data?
What is the r for the data?
What does correlation say about causation?
Predict a Lab Report Score for someone who spent one hour on it.
Not to be used, posted, etc. without my expressed permission.B Heard
5. Predicted score for someone who spent one hour would be:
y = 3.158(1) +24.71
y = 27.9 or I would say 28 since all scores are in whole numbers
Also, correlation says nothing about causation!
Not to be used, posted, etc. without my expressed permission.B Heard
6. Stronger Positive Correlation
Stronger Negative Correlation
0
+1
-1
r
Not to be used, posted, etc. without my expressed permission.B Heard
7. Know the difference between Binomial and Poisson
Remember we talked about this in a previous lecture!
8. A State Trooper notes that at a certain intersection, an average of three cars run the red-light per hour. What is the probability that the next time he is there exactly two cars run the red-light?

Poisson with average of 3. want P(2) P(2) = .2240(Use Excel or Excel Template)
Final Exam Review
9. The probability that a house in a neighborhood has a dog is 40%. If 50 houses in the neighborhood are randomly selected what is the probability thatone (or a certain number) of the houses will have a dog?

a.Is this a binomial experiment?

b. Use the correct formula to find the probability that, out of 50 houses, exactly 22 of the houses will have dogs. Show your calculations or explain how you found the probability.
Answer Follows
Final Exam Review
10. a) Fixed number of independent trials, only two possible outcomes in each trial {S,F} (dog or not), probability of success is the same for each trial, and random variable x counts the number of successful trials. So YES it is.

b) n = 50; p = .40 = P(success) = house has a dogWe want P(22) --> P(22) = .0959 (I used a Binomial Template) (Also be able to use the at least column etc.)
Final Exam Review
11. Know basic terms like mean, median, mode, standard deviation, variance, etc.
Mean is the average
Median is the center
Mode is the most frequently occurring
Know the variance is the standard deviation squared
Know the standard deviation is the square root of the variance
12. Be able to understand the normal distribution and how it relates to the mean, standard deviation, variance, etc.
For example, I did an analysis and found the mean number of failures was 7 and the standard deviation was 1.5. Answer the two questions below.
How many standard deviations is 10 from the mean?10 7 = 3, 3/1.5 = 2 (your answer)
How many standard deviations is 6.25 from the mean? 6.25 7 =- .75,- .75/1.5 = -0.5 (your answer)
Final Exam Review
13. Be able to use the Standard Normal Distribution Tables or
Excel to find probability values and z scores.
Examples:
Find the following probability involving the Standard Normal Distribution. What is P(z -.60)?
1 0.2743 =0.7257(using table or Excel 1 =NORMDIST(-0.6,0,1,TRUE))
Final Exam Review
See Following Charts
14. Explanation
Go to Template Site
http://highered.mcgraw-hill.com/sites/0070620164/student_view0/excel_templates.html
Save Normal Distribution File to your computer
Open the file and make sure you Unprotect as I described in previous presentations
Take out all the values in the green cells
15. Explanation
I put 0 in for the mean and 1 for the standard deviation.
I worked the first one on the top left and the second on the top middle. (Only input into green cells)
16. The mean number of teachers in a Virginia public school is said to be 42.7.A hypothesis test is performed at a level of significance of 0.05 and a P-value of .06.How would you interpret this?
Final Exam Review
17. The mean number of teachers in a Virginia public school is said to be 42.7.A hypothesis test is performed at a level of significance of 0.05 and a P-value of .06.How would you interpret this?
Fail to reject the null hypothesis, because there is not enough evidence to reject the claim that there are 42.7 teachers per school.
Final Exam Review
18. I am buying parts for a new project.I have two vendors to choose from.Vendor X has a customer satisfaction rating of 8.7 with a standard deviation of 1.9.Vendor Y has a customer satisfaction rating of 8.6 with a standard deviation of 0.2Which should I choose?
Final Exam Review
19. I am buying parts for a new project.I have two vendors to choose from.Vendor X has a customer satisfaction rating of 8.7 with a standard deviation of 1.9.Vendor Y has a customer satisfaction rating of 8.6 with a standard deviation of 0.2Which should I choose?
I think I would go with Vendor Y who seems to be more consistent (standard deviation)
Final Exam Review
20. I am playing a game that has four different outcomes in terms of how much money I could win.Determine my expected gain if I played this game 5 times.
Outcomes/Probability $10 (10%),$6 (20%),$2 (30%), $1 (40%)
Final Exam Review
21. I am playing a game that has four different outcomes in terms of how much money I could win.Determine my expected gain if I played this game 5 times.
Outcomes/Probability $10 (10%),$6 (20%),$2 (30%), $1 (40%)
10(0.10)+6(0.20) + 2(0.30) + 1 (0.40) = $3.20
For five times it would be 5($3.20) = $16.00
Final Exam Review
22. How would you describe the following stem and leaf plot?
2|5
3|2
4|1899
5|13668
6|0227
Not to be used, posted, etc. without my expressed permission.B Heard
23. How would you describe the following stem and leaf plot?
2|5
3|2
4|1899
5|13668
6|0227
Skewed to the Left
Not to be used, posted, etc. without my expressed permission.B Heard
24. Determine the minimum required sample size if you want to be 90% confident that the sample mean is within 5 units of the population mean given sigma = 8.4. Assume the population is normally distributed.
Final Exam Review
25. Determine the minimum required sample size if you want to be 90% confident that the sample mean is within 5 units of the population mean given sigma = 8.4. Assume the population is normally distributed.
n = (Zc*sigma/E)^2 = [(1.645 * 8.4)/ 5]^2 = (2.7636)^2= 7.64= 8 (always round up sample sizes)
Final Exam Review
Covered in Week 7 Lecture
26. Scores on an exam for enteringa military training program are normally distributed, with a mean of 60 and a standard deviation of 12. To be eligibleto enter, a person must score in the top 15%. What is the lowest score you can earn and still be eligible to enter?
mu = 60; sigma = 12we want top 15% or an area greater than 1 -.15or .85z = 1.04 ---> x =(1.04)(12) + 60 = 72.48 orneed a score of 73 (Round it up)
Final Exam Review
Use Normal Template
Explanation follows
27. Explanation
I put 60 in for the mean and 12 for the standard deviation.
Put in 0.15 for the bottom middle to get 72.44 (remember to round up to 73).
28. An airplane has 50 passengers.There are 4 celebrities on the plane.How many ways can a reporter choose 3 of these passengers at random and not pick a celebrity?
Final Exam Review
29. An airplane has 50 passengers.There are 4 celebrities on the plane.How many ways can a reporter choose 3 of these passengers at random and not pick a celebrity?
This isa Combination 46C3 which is 15180
Final Exam Review
30. The average (mean) monthly grocery cost for a family of 4 is $600. The distribution is known to be normal with a standard deviation =60. A family is chosen at random. a) Find the probability that the familys monthly grocery cost purchases will be between $550 and $650.b)Find the probability that the familys monthly grocery cost purchases will be less than $700.c) What is the probability that the familys monthly grocery cost purchases will be more than$630?
Answers follow
Final Exam Review
31. Using Tables or EXCEL (I used an Excel Template like one I showed you):a) P(550 < x < 650) = 0.5953b) P(x < 700) =.9522 c) P(x > 630) = .3085
Final Exam Review
See Following Charts,
Use Normal Template
32. Explanation
I put 600 in for the mean and 60 for the standard deviation.
I worked the part a on the top right, part b on the top left and part c on the top middle. (Only input into green cells AND dont forget to hit the Enter key)
33. As an instructor, I have been collecting data to see if I can model a students performance on a standardized entrance exam.I determined that the multiple regression equationy = -250+ 16a + 30b, where a is a students grade on a quiz, b is the students rank on a class list, gives y, the score on a standardized entrance exam. Based on this equation, what would the standardized entrance exam score for a student who makes a 7 on the quiz and had a ranking of 1