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NEED TO HAVE STATISTIC HOMEWORK DONE 5/11/13 BY 12 MIDNIGHT..NEED SOME WHO IS GOOD AT STATISTIC…THANKS
Answer all
3
0
questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted.
Refer to the following frequency distribution for Questions
1
,
2
, 3, and
4
.
The frequency distribution below shows the distribution for suspended solid concentration (in ppm) in river water of
5
0
different rivers collected in September
20
12
.
|
Concentration (ppm) |
Frequency |
|||||
| 20 |
– 29 |
1 | ||||
| 30 |
– 39 |
7 |
||||
|
40 |
– 49 |
11 |
||||
| 50 |
– 59 |
8 |
||||
|
60 |
– 69 |
|||||
|
70 |
– 79 |
|||||
|
80 |
– 89 |
3 | ||||
|
90 |
– 99 |
2 |
1. What percentage of the rivers had suspended solid concentration at most 49?
(5 pts)
2. Calculate the mean of this frequency distribution.
(
10
pts)
3. In what class interval must the median lie? Explain your answer. (You don’t have to
find the median)
4. Assume that the smallest observation in this dataset is 28. Suppose this observation were incorrectly recorded as 2.8 instead of 28. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers. (5 pts)
Refer to the following information for Questions 5 and 6.
A fair die is rolled 2 times. Let A be the event that the outcome of the first roll is an odd number. Let B be the event that the outcome of second roll is at least 5.
5. What is the probability that the outcome of the second roll is at least 5, given that the first roll is
an odd number?
(10 pts)
6. Are A and B independent? Why or why not?
(5 pts)
Refer to the following data to answer questions 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.
A random sample of song playing times in seconds is as follows:
231 220 2
13
230 293
7. Find the standard deviation.
(10 pts)
8. Are any of these playing times considered unusual in the sense of our textbook? Explain.
Does this differ with your intuition? Explain.
(5 pts)
Refer to the following situation for Questions 9, 10, and 11.
The five-number summary below shows the grade distribution of two STAT 200 quizzes.
|
Minimum |
Q1 |
Median |
Q3 |
Maximum |
|
Quiz 1 |
12 |
95 |
100 |
|
|
Quiz 2 |
35 |
For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. Then
explain your answer in each case.
(5 pts each)
9. Which quiz has greater interquartile range in grade distribution?
10. Which quiz has the greater percentage of students with grades 80 and over?
11. Which quiz has a greater percentage of students with grades less than 60?
12.
A random sample of 225 SAT scores has a mean of 1522. Assume that SAT scores have a
population standard deviation of 300. Construct a 95% confidence interval estimate of the mean SAT scores.
(15 pts)
Refer to the following information for Questions 13 and 14.
There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 95 people; the roster of the Statistics class shows 86 people. There are 43 overachieving seniors on both rosters.
13. What is the probability that a randomly selected senior is in exactly one of the two classes
(but not both)?
(10 pts)
14. If the student is in the Calculus class, what is the probability the student is also in the
Statistics class?
(10 pts)
Refer to the following information for Questions 15, 16, and
17
.
A box contains 10 chips. The chips are numbered 1 through 10. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in all from this box.
|
15. |
How many elements are in the sample space of this experiment? |
|
16. |
What is the probability that the three numbers drawn are all different? |
|
17. |
What is the probability that the three numbers drawn are all even numbers? |
Questions
18
and 19 involve the random variable x with probability distribution given below.
|
x |
4 | 10 | |||
|
P(x) |
0.1 |
0.2 |
0.4 |
18. Determine the expected value of x.
(10 pts)
19. Determine the standard deviation of x.
(10 pts)
Consider the following situation for Questions 20 and 21.
Airline overbooking is a common practice. Due to uncertain plans, many people cancel at the last minute or simply fail to show up. Capital Air is a small commuter airline. Its past records indicate that 85% of the people who make a reservation will show up for the flight. The other 15% do not show up. Capital Air decided to book 11 people for today’s flight. Today’s flight has just 10 seats.
20. Find the probability that there are enough seats for all the passengers who show up. (Hint: Find
the probability that in 11 people, 10 or less show up.)
(10 pts)
21. How many passengers are expected to show up?
(5 pts)
22. Given a sample size of 65, with sample mean 720 and sample standard deviation 85, we perform the following hypothesis test. H0 :µ =750
H1 :µ <750
What is the conclusion of the test at the a = 0.05 level? Explain your answer.
(20 pts)
Refer to the following information for Questions 23, 24, and 25.
The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
23. What is the probability that a randomly person has an IQ between 85 and 115? (10 pts)
24. Find the 90th percentile of the IQ distribution.
(5 pts)
25. If a random sample of 100 people is selected, what is the standard deviation of the sample mean? (5 pts)
26. Consider the hypothesis test given by
:
530
p =
:
530.
p ≠
In a random sample of 85 subjects, the sample mean is found to be x = 522.3. Also, the population standard deviation is ó = 29.
Determine the P-value for this test. Is there sufficient evidence to justify the rejection of
H0 at the á = 0.01 level? Explain.
(20 pts)
27. In a nationwide study directed by UMUC Teaching Hospital, 780 persons with stable heart disease were treated. Half of the subjects were treated with drugs and half underwent bypass surgery. After 6 years, 351 of those treated with drugs and 359 of those who underwent bypass surgery were still alive.
At the 0.05 significance level, is there sufficient evidence to support the claim that surgery is more effective than drugs? Show all work and justify your answer.
(25 pts)
28. The UMUC Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color
distribution is correct. Show all work and justify your answer.
(25 pts)
|
Color |
Brown |
Yellow |
Orange |
Green |
Tan |
|
Number |
45 |
13 | 17 | 18 |
Refer to the following data for Questions 29 and 30. :
|
x |
0 |
– 1 |
|
y |
– 2 |
5 |
29. Is there a linear correlation between x and y at the 0.05 significance level? Justify your
answer.
(10 pts)
30. Find an equation of the least squares regression line. Show all work; writing the correct
equation, without supporting work, will receive no credit.
(15 pts)
STAT200 : Introduction to Statistics
STAT200 : Introduction to Statistics Page 3 of 5
STAT200 : Introduction to Statistics Page 4 of 5
STAT200 : Introduction to Statistics Page 5 of 5
H0 H1
