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“###
San Jose State University
Department of Applied Data Science\n”,
“#
DATA 220
Mathematical Methods for Data Analysis\n”,
“###
Spring 2020
Instructor: Ron Mak\n”,
“#
MIDTERM EXAMINATION\n”,
“####
Each problem is worth 10 points.
200 points total
Don't use plagiarized sources. Get Your Custom Essay on
in python for data visualization using numpy and pandas
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You have until 8:00 PM to complete this exam and submit it to Canvas.
Take a break afterward and come back for a short lecture at 8:15.
Open book, notes, and internet.
Individual work only! No communications with anyone else during the exam.
Write your solution in one or more cells after each problem.
Always show your work.
You can use Python library functions
or write your own functions and other support code.
”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“
\n”,
“\n”,
“#### A survey asked 125 families about their internet access. The following table contains the results:\n”,
“
\n”,
”
\n”,
”
Race |
\n”,
”
Internet access |
\n”,
”
No Internet |
\n”,
”
Total |
\n”,
”
\n”,
”
\n”,
”
Caucasian |
15 |
22 |
37 |
\n”,
”
\n”,
”
\n”,
”
Asian |
23 |
18 |
41 |
\n”,
”
\n”,
”
\n”,
”
Hispanic |
14 |
33 |
47 |
\n”,
”
\n”,
”
\n”,
”
Total |
52 |
73 |
125 |
\n”,
”
\n”,
“
\n”,
“\n”,
“#### Randomly select a family from the survey.”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 1.a. What is the probability that the selected family has internet access?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 1.b. What is the probability that the selected family is Asian?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 1.c. What is the probability that the selected family has internet access and is Asian?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 1.d. What is the probability that the selected family has internet access or is Asian?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“
\n”,
“\n”,
“#### Two tennis-playing friends, Deborah and Robert, keep track of who won their games based on the lengths of their pregame warm-up times:\n”,
“
\n”,
”
\n”,
”
Warm-up time |
\n”,
”
Deborah wins |
\n”,
”
Robert wins |
\n”,
”
Total |
\n”,
”
\n”,
”
\n”,
”
Short |
4 |
6 |
10 |
\n”,
”
\n”,
”
\n”,
”
Long |
16 |
24 |
40 |
\n”,
”
\n”,
”
\n”,
”
Total |
20 |
30 |
50 |
\n”,
”
\n”,
“
”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 2.a. What is the probability that Deborah wins the next game if she had a short warm-up time?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 2.b. Deborah won the last game! What is the probability that she had a short warm-up time before the game?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 2.c. Given that the warm-up time was long, what is the probability that Robert will win the next game?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 2.d. Can Deborah correctly claim that she has a better chance of winning a game if the warm-up time was long?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“
\n”,
“\n”,
“#### The number of cars at a local dealership:\n”,
“
\n”,
”
\n”,
”
|
\n”,
”
Sedan |
\n”,
”
SUV |
\n”,
”
Total |
\n”,
”
\n”,
”
\n”,
”
New |
24 |
15 |
39 |
\n”,
”
\n”,
”
\n”,
”
Used |
9 |
12 |
21 |
\n”,
”
\n”,
”
\n”,
”
Total |
33 |
27 |
60 |
\n”,
”
\n”,
“
”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 3.a. What is the probability that a randomly selected car from the dealership is new, given that it is a sedan? Calculate your answer directly using conditional probability.”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 3.b. Recalculate your answer to Problem 3.a but this time, use Bayes’ Theorem.”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“
\n”,
“\n”,
“#### Pounds of trash generated each day by ten households (assume that the population is normally distributed):\n”,
“
\n”,
”
\n”,
”
Pounds of trash |
\n”,
”
\n”,
”
\n”,
”
3.9 |
4.6 |
15.6 |
10.5 |
16.0 |
\n”,
”
6.7 |
12.0 |
9.2 |
13.8 |
16.8 |
\n”,
”
\n”,
“
”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 4. Construct a 95% confidence interval for the mean based on the sample.”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“
\n”,
“\n”,
“#### PROBLEM 5. Suppose that 60% of the students are female in the Department of Applied Data Science. What is the probability that a department seminar of 10 students will have exactly 4 female students?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 6. The Department of Applied Data Science gives a qualifying exam to applicants for admission. 60% of the applicants pass the exam and are admitted as students, and 80% of them sucessfully graduate. Because of doubts about the reliability of the exam, the department conducted an experiment where it admitted a random sample of applicants who did not pass the exam, and only 50% of those students sucessfully graduated. If the department decided to stop giving the exam, what percentage of admitted applicants would you expect to sucessfully graduate?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 7. Applied Data Science students used machine learning to train a program to grade essay exams and deployed the program on the web. It can grade three exams in a five-minute period, and exams have been submitted to it at an averate rate of 1.2 exams every five minutes. What is the probability that more exams than the program can grade will be submitted in the next five minutes?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 8. A sample of 36 data scientists have an average age of 41.7 years with a sample standard deviation of 6.9 years. What is a 95% confidence interval to estimate the average age of a data scientist?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 9. The NBA teams with the 13 worst records at the end of the season participate in a lottery to determine the order in which to draft new players for the next season. How many different arrangements for the drafting order are there for these 13 teams?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 10. After getting your data science degree, your dream job is to work for Amalgamated Number Crunchers, Inc. You believe you have a 60% chance of getting hired by them. Historically, 75% of ANC new hires had two interviews, and 45% of the unsuccessful candidates also had two interviews. What is the probability that you will be hired, given that you’ve just had two interviews?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 11. How many different panels of 12 jurors for a trial can be selected from a group of 50 people?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“
\n”,
“\n”,
“#### Prof. Mak claims that the average score on his final exams will not be 70. At the end of the school year, a random sample of 45 of his students had an average score of 72.6 with a standard deviation of 14.1.”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 12.a. What are the null and alternative hypotheses?”
]
},
{
“cell_type”: “markdown”,
“metadata”: {},
“source”: [
“#### PROBLEM 12.b. At the 0.01 level of significance, what can you conclude about Prof. Mak’s claim? Explain and show your work, such as by printing intermediate values from your calculation.”
]
}
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