Download Homework due 3/14/2017

Community College of Denver
Course: MAT135 –Statistics
Instructor: Vikki French
[email protected]
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Homework due 3/14/2017
Reading assignment for next class: none! Yay!
Proportions
Assume a sample of 200 college students is representative of all college students
The number of students in the sample who used marijuana in the past 6 months is 80
1) What is the research question?
2) Is the random variable binomial?
3) What is “success”?
4) What is n?
5) What is x?
6) What is p̂?
7) What is your best estimate of p?
8) What is your best estimate of q?
9) Is the sample size large enough to use the normal distribution to calculate
probabilities? Why or why not?
10) What is the standard error of p̂?
11) What will be the normal curve
for p̂?
_______ _______ _______
_______
_______ _______ _______
12) What is the probability the true proportion of students who used marijuana in the
past 6 months is between 33.07% and 46.93%?
13) What is the probability that the percentage of students in that sample who have
used marijuana in the past 6 months is less than 32%?
14) Is it very likely that the true percentage of students who have used marijuana in the
past 6 months is less than 32%?
15) What is the probability that the percentage of students in that sample who have
used marijuana in the past 6 months is greater than 50%?
16) Is it very likely that the true percentage of students who have used marijuana in the
past 6 months is greater than 50%?
Practice Problems for Exam 2
(No guarantee at this point that it will look like the Exam…)
5.1
Suppose you roll a single dice once, and record the # that faces up.
So X is the random variable = {1,2,3,4,5,6}
1) P(3) =
2) P(Even number) =
3) P(# greater than 1) =
4) P(2 or 5) =
5) P(at most 4) =
6) What kind of Probability (Classical (assumes equal likelihood), Relative Frequency
(what you observe), or Subjective (based on experience)) were you using to answer
the questions?
6.1
X = # of people in line at registration window
All possible outcomes are shown
7) What is the probability of 3 people in line?
8) What is the probability that at least 1 person will be
waiting in line?
# in Line
0
1
2
3
Probability
.087
.259
.175
?
9) What is the probability that at most 2 people will be waiting in line?
10) What is the probability that 0 or 2 people will be waiting in line?
11) Compute the mean of this distribution (multiply each value x by its probability, then
add these values up)
12) Is the mean the same as the most likely outcome?
13) Compute the z-score for the outcome of 0 people waiting in line:
5.2/5.3/5.4
Suppose we randomly select
someone from the table:
14) Create the probability
table:
15) Find the probability that
person is a Broncos fan:
# of siblings
0-2
3-5
6 or more
Broncos Fan
5
6
3
Not a Broncos Fan
1
2
7
# of siblings
Broncos Fan
Not a Broncos Fan
0-2
3-5
6 or more
16) Find the probability that
person has 6 or more siblings:
17) Find the probability that person is a Broncos fan and has 3-5 siblings:
18) Find the probability that person is a Broncos fan OR has 0-2 siblings:
19) Given they are a Broncos fan, what is the probability they have 3-5 siblings?
20) Given they have 3-5 siblings, what is the probability they are a Broncos fan?
21) What is the probability that a Broncos fan has 6 or more siblings?
6.2
Suppose 53% of Auraria students drive to campus
Suppose we randomly sampled 15 students and recorded the number that drove to
campus
22) What is a success?
23) What is n=?
24) What is p=?
25) Find: P(less than 5 drive)
7.1-7.2
26) Area under a curve will be interpreted as ____________
27) The total area under any normal curve = __________
28) When you draw a normal curve, what ALWAYS goes in the middle____________
29) What is the area to the right(above) of the mean?
30) What is the area to the left(below) of the mean?
The mean of the SAT Math section is 500 with a standard deviation of 100
The scores are normally distributed
31) What is the probability that an individual will score above 650?
32) What is the probability that an individual will score below 475?
33) What percent of individuals will score at least 700?
34) What is the probability that an individual will score between 415 and 635?
35) Suppose an individual scores 680 on the exam. What is his/her percentile rank?
36) What score represents the 90th percentile for this test?
37) What score is the cutoff for the top 1% who take this test?
38) What score is the cutoff for the bottom 25% who take this test?
39) What scores are the cutoffs for the middle 95% who take this test?
8.1
Not every population of data is Normal (bell shaped)
There are many distributions that are skewed right, skewed left, or some other shape
However, the central limit theorem for means is so strong, that as the sampling size
increases, the distribution of sample means becomes more bell shaped(normal)
40) If you do not know the shape of the population distribution, what is the minimum
sample size needed for the distribution of sample means to be normal?
41) Suppose we sample n = 23 from a population that is normal
Can we apply the central limit theorem?
42) Suppose we sample n = 17 from a population that is not normal
Can we apply the central limit theorem?
43) Suppose we sample n = 35 from a population that is normal.
Can we apply the central limit theorem?
44) If you were a researcher collecting a sample mean, and you didn’t know the shape
of the population distribution, what must you make sure you do to use the central
limit theorem?
8.2
45) The census bureau reports that 12% of the population is left-handed
You sample 100 people and ask if they are left-handed or not
up =
σp =
46) P(observing 15 or more left handed people out of the sample of 100) =
The census bureau reports that 68% of the population owns a smartphone
You sample 100 people and ask if they own a smartphone or not
47) up =
48) σp =
49) P(observing 60 or less smartphone owners out of the sample of 100) =