stat quiz
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stat_021.zipSTAT 021 Final Exam.docx
Applied Statistics
Final Exam
Notes:
· Do not unnecessarily smile at the person sitting next to you, they may also not know the answer.
· If you have missed my classes and have not prepared, don’t waste your time, instead pray to God.
· It’s good to have a lot of beautiful options in life but all questions are compulsory here.
1. For the following list of numbers, calculate the average and the standard deviation : 2, 6, 8, 10, 14
2. True or False. If you add 7 to each entry on a list, that adds 7 to the average.
3. True or False. If you add 7 to each entry on a list, that adds 7 to the standard deviation.
4. True or False. If you double each entry on a list, that doubles the average.
5. True or False. If you double each entry on a list, that doubles the standard deviation.
6. True or False. If you change the sign of each entry on a list, that changes the sign of the average.
7. True or False. If you change the sign of each entry on a list, that changes the sign of the standard deviation.
8. Someone claims to be able to predict the toss of a coin. You decide to test her powers by tossing a coin eight times and counting the number of correct guesses. If in fact she is bluffing and her guesses are random, what is the chance that she gets six or more tosses correct?
9. Which of the following is more likely? Explain intuitively.
a. A fair coin is tossed 25 times and 10 or more of these tosses are heads.
b. A fair coin is tossed 50 times and 20 or more of these tosses are heads.
10. A town contains 6000 families, each with three children.
a. In any single family, what is the chance of getting two girls and a boy?
b. In a town of 6,000, what is the chance that 2,325 or more families would have two girls and a boy? Set this counting process up as a box model. Draw the box model. And calculate the chance.
11. A class of 400 students is divided into 2 sections of 200 each. Both sections are given a common exam. The following is observed
|
|
Average |
SD |
|
Section 1 |
85 |
10 |
|
Section 2 |
45 |
10 |
Suppose all 400 scores are combined as one list. The SD of the new list will be
i. smaller than 10
ii. larger than 10
iii. equal to 10
iv. can't tell without knowing the entire list
12. A teaching assistant gives a quiz. There are 10 questions on the quiz and no partial credit is given. After grading the papers the TA writes down for each student the number of questions the student got right and the number he got wrong. The average number of correct answers is 6.4 with an SD of 2.0.
a. What is the average and SD of the number of wrong answers? ____________Average ____________SD
b. The correlation coefficient between the numbers of right and wrong answers is
i. 0
ii. -.5
iii. +.5
iv. -1
v. +1
vi. can't tell
13. A doctor records, for 400 hospital patients selected at random, the pair: (temperature when admitted, temperature 24 hours later). He finds that the average temperatures are 101 degrees when admitted, 99 the next day. The SD is 1.5 degrees for temperatures when admitted, 0.5 for those the next day. The correlation between the two temperatures is 0.8. The scatter diagram is football shaped.
a. if a patient enters with temperature 103, what do you expect his temperature to be the next day?
b. The fact that the average temperature the day after entering is 2 degrees less than upon admission is due to the regression effect. True or False?
14. In a city, 20% of the workers have incomes over $40,000 per year. If 1600 workers are chosen at random with replacement, what is the chance that between 320 and 336 of those chosen have incomes over $40,000 per year?
15. 5. A coin is tossed n times. There is about 95% chance that the proportion of heads is in the range .49 to .51. The number of tosses n is closest to:
a. 1,000
b. 5,000
c. 10,000
d. 50,000
STAT 021 Midterm.docx
Mid-Term
Q1. There are 26 letters in the English alphabet; A, E, I, O, and U are vowels; the rest are consonants. A box contains the letters O, R, A, N, G, E, S. Three letters are drawn at random with replacement. Find the chance that
a) all the letters drawn are consonants
b) not all the letters drawn are vowels
c) at least one of the letters drawn is a vowel
Q2. Three draws are made at random without replacement from a box which contains 4 red tickets, 4 blue tickets, and 2 green tickets. The conditional chance that all three draws are the same color, given that the first two are red, is
(i) (4/10)x(3/9)x(2/8)
(ii) 2/8
(iii) other (specify): ______________
Q3. A box contains the letters O, R, A, N, G, E, S. Letters are drawn one by one at random without replacement until the box is empty. Find the chance that
a) the letter R appears on the last draw: _____________
b) the letter R appears on the last draw, given that a vowel appeared on the first draw:______________
c) vowels appear on the first two draws: ______________
d) there is one vowel and one consonant among the first two letters drawn: _____________
Q4. In an undergraduate class, 70% of the students are juniors and the rest are seniors. Of the juniors, 40% are math majors. Of the seniors, 25% are math majors. One student is picked at random. Find
a) P(junior) b) P(senior) c) P(math major | junior)
d) P(not a math major | junior) e) P(math major | senior)
f) P(not a math major | senior) g) P(junior math major)
h) P(senior math major) i) P(math major)
j) P(junior | math major) k) P(senior | math major)
l) P(junior | not a math major)
Q5. An electrical firm manufactures light bulbs that have a life, before burn-out, that is normally distributed with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that a bulb burns between 778 and 834 hours.
Q6. Suppose that 10% of a given population has benign chronic flatulence. Suppose that there is a standard screening test for benign chronic flatulence that has a 90% chance of correctly detecting that one has the disease, and a 10% chance of a false positive (erroneously reporting that one has the disease when one does not). We pick a person at random from the population (so that everyone has the same chance of being picked) and test him/her. The test is positive. What is the chance that the person has the disease?
