07 Jan Find the probability of correctly

Module 1 – Case

INTRODUCTION TO PROBABILITY

Case Assignment

By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results.

In a poll, respondents were asked if they have traveled to Europe. 68 respondents indicated that they have traveled to Europe and 124 respondents said that they have not traveled to Europe. If one of these respondents is randomly selected, what is the probability of getting someone who has traveled to Europe?

The data set represents the income levels of the members of a golf club. Find the probability that a randomly selected member earns at least $100,000.

INCOME (in thousands of dollars)

98 102 83 140 201 96 74 109 163 210

81 104 134 158 128 107 87 79 91 121

A poll was taken to determine the birthplace of a class of college students. Below is a chart of the results.

What is the probability that a female student was born in Orlando?

What is the probability that a male student was born in Miami?

What is the probability that a student was born in Jacksonville?

Gender Number of students Location of birth

Male 10 Jacksonville

Female 16 Jacksonville

Male 5 Orlando

Female 12 Orlando

Male 7 Miami

Female 9 Miami

Of the 538 people who had an annual check-up at a doctor’s office, 215 had high blood pressure. Estimate the probability that the next person who has a check-up will have high blood pressure.

Find the probability of correctly answering the first 4 questions on a multiple choice test using random guessing. Each question has 3 possible answers.

Explain the difference between independent and dependent events.

Provide an example of experimental probability and explain why it is considered experimental.

The measure of how likely an event will occur is probability. Match the following probability with one of the statements. There is only one answer per statement.

0 0.25 0.60 1

a. This event is certain and will happen every time.

b. This event will happen more often than not.

c. This event will never happen.

d. This event is likely and will occur occasionally.

Flip a coin 25 times and keep track of the results. What is the experimental probability of landing on tails? What is the theoretical probability of landing on heads or tails?

A color candy was chosen randomly out of a bag. Below are the results:

Color Probability

Blue 0.30

Red 0.10

Green 0.15

Yellow 0.20

Orange ???

a. What is the probability of choosing a yellow candy?

b. What is the probability that the candy is blue, red, or green?

c. What is the probability of choosing an orange candy?

Submit your work by the module due date. If you are having difficulty, contact your professor.

Module 1 – SLP

INTRODUCTION TO PROBABILITY

By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

The assignment this week is to collect quantitative data for a minimum of 10 days from ONE of your daily activities. Some examples of data collection include:

The number of minutes you spend studying every day.

The time it takes to cook meals each day.

The amount of daily time spent talking on the phone.

The amount of time you drive each day.

In a paper (1–3 pages), describe the data you are going to collect and how you are going to keep track of the time. Within the paper, incorporate the concepts we are learning in the module, including (but not limited to) probability theory, independent and dependent variables, and theoretical and experimental probability. Discuss your predictions of what you anticipate the data to look like and events that can skew the data. Collect data for at least 10 days. Include at least 3-5 days of data with your SLP 1 submission. Continue collecting data for the remaining days for use in SLP 2. Do you think the data will provide a valid representation of these activities? Explain why or why not.

Submit your paper at the end of Module 1. Future SLP assignments depend on this data and thus this assignment needs to be completed early in the session.

SLP Assignment Expectations

Answer all questions posted in the instructions. Use information from the modular background readings and videos as well as any good-quality resource you can find. Cite all sources in APA style and include a reference list at the end of your paper.

Note about page length: Your ability to clearly articulate and explain these concepts is being assessed. The page length is a general guideline. A 3- or 4-page paper does not necessarily guarantee a grade of “A.” An “A” paper would include detailed information and explanations of all the assignment requirements listed above. The letter grade will be based upon demonstrated mastery of the content and ability to articulate and apply the concepts in the assignment. Keep this in mind while writing your paper.

Module 2 – Case

MEASURES OF CENTRAL TENDENCY

Case Assignment

By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results.

Describe the measures of central tendency. Under what condition(s) should each one be used?

Last year, 12 employees from a computer company retired. Their ages at retirement are listed below. First, create a stem plot for the data. Next, find the mean retirement age. Round to the nearest year.

55 77 64 77 69 63 62 64 85 64 56 59

A retail store manager kept track of the number of car magazines sold each week over a 10-week period. The results are shown below.

27 30 21 62 28 18 23 22 26 28

Find the mean, median, and mode of newspapers sold over the 10-week period.

Which measure(s) of central tendency best represent the data?

Name any outliers.

Joe wants to pass his statistics class with at least a 75%. His prior four test scores are 74%, 68%, 84% and 79%. What is the minimum score he needs on the final exam to pass the class with a 75% average?

Nancy participated in a summer reading program. The number of books read by the 23 participants are as follows:

10 9 6 2 5 3 9 1 6 3 10 4 7 6 3 5 6 2 6 5 3 7 2

Number of books read Frequency

1–2

3–4

5–6

7–8

9–10

Complete the frequency table.

Find the mean of the raw data.

Find the median of the raw data.

The chart below represents the number of inches of snow for a seven-day period.

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

2 5 3 10 0 4 2

Find the mean, median, and mode.

Which is the best measure of central tendency?

Remove Wednesday from the calculations. How does that impact the three measures of central tendency?

Describe the effect outliers have on the measures of central tendency.

A dealership sold 15 cars last month. The purchase price of the cars, rounded to the nearest thousand, is represented in the table.

Purchase price Number of cars sold

$15,000 3

$20,000 4

$23,000 5

$25,000 2

$45,000 1

Find the mean and median of the data.

Which measure best represents the data? Use the results to support your answer.

What is the outlier and how does it affect the data?

8. What do the letters represent on the box plot?

Box plot

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9. The test scores from a math final exam are as follows:

64 85 93 55 87 90 73 81 86 79

Create a box plot using the data.

Label the five points on the box plot and include numerical answers from part “a.”

10. Using the data and results from Question 9, answer the following questions.

What is the median?

What is the range?

What is the interquartile range?

In a short paragraph, describe the data in the box plot.

Submit your work by the module due date. If you are having difficulty, please contact your professor.

Module 2 – SLP

MEASURES OF CENTRAL TENDENCY

By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Using the data you collected in the Module 1 SLP, write a paper (1–3 pages) including all of the following content:

Calculate the mean, median, and mode of your collected data. Show and explain your calculations.

Are these numbers higher or lower than you expected? Explain.

Which of these measures of central tendency do you think most accurately describes the variable you are looking at? Provide your justification.

Create a box plot to represent the data, labeling and numerating all 5 points on the box plot. For the plot, you may draw and insert it in your paper as a picture. Make sure it is legible.

Submit your paper at the end of Module 2.

SLP Assignment Expectations

Answer all questions posted in the instructions. Use information from the modular background readings and videos as well as any good-quality resource you can find. Cite all sources in APA style and include a reference list at the end of your paper.

Note about page length: Your ability to clearly articulate and explain these concepts is being assessed. The page length is a general guideline. A 3- or 4-page paper does not necessarily guarantee a grade of “A.” An “A” paper would include detailed information and explanations of all the assignment requirements listed above. The letter grade will be based upon demonstrated mastery of the content and ability to articulate and apply the concepts in the assignment. Keep this in mind while writing your paper.

Module 3 – Case

FREQUENCY DISTRIBUTIONS

Case Assignment

By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results.

The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?

99 34 86 57 73 85 91 93 46 96 88 79 68 85 89

The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?

If you know the standard deviation, how do you find the variance?

To get the best deal on a stereo system, Louis called 8 out of 20 appliance stores in his neighborhood and asked for the cost of a specific model. The prices he was quoted are listed below:

$216 $135 $281 $189 $218 $193 $299 $235

Find the standard deviation.

A company has 70 employees whose salaries are summarized in the frequency distribution below.

Salary Number of Employees

5,001–10,000 8

10,001–15,000 12

15,001–20,000 20

20,001–25,000 17

25,001–30,000 13

Find the standard deviation.

Find the variance.

6. Calculate the mean and variance of the sample data set provided below. Show and explain your steps. Round to the nearest tenth.

14, 16, 7, 9, 11, 13, 8, 10

Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)

3, 5, 1, 6, 1, 2, 2, 6, 3, 4, 5, 1, 1, 3, 4, 2, 1, 6, 5, 3, 4, 2, 1, 3, 2, 4, 6, 5, 3, 1

Answer the following questions using the frequency distribution table you created in No. 7.

Which number(s) had the highest frequency?

How many times did a number of 4 or greater get thrown?

How many times was an odd number thrown?

How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?

The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the data below, find the following for each sample.

Range

Standard deviation

Variance

Lastly, compare the two sets of results.

Company Wait times in seconds

Big Burger Company 105 67 78 120 175 115 120 59

The Cheesy Burger 133 124 200 79 101 147 118 125

What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?

Submit your work by the module due date. If you are having difficulty, please contact your professor.

Module 3 – SLP

FREQUENCY DISTRIBUTIONS

By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Continuing with the data you collected in the Module 1 SLP, write a paper (1–3 pages) including all of the following content:

Include your data from Module 1.

Create a frequency distribution table for your data. You can use Excel or Word.

Calculate the standard deviation.

Calculate the variance.

Is this a normal distribution? How do you know?

What are the implications?

Submit your paper at the end of Module 3.

SLP Assignment Expectations

Answer all questions posted in the instructions. Use information from the modular background readings and videos as well as any good-quality resource you can find. Cite all sources in APA style and include a reference list at the end of your paper.

Note about page length: Your ability to clearly articulate and explain these concepts is being assessed. The page length is a general guideline. A 3- or 4-page paper does not necessarily guarantee a grade of “A.” An “A” paper would include detailed information and explanations of all the assignment requirements listed above. The letter grade will be based upon demonstrated mastery of the content and ability to articulate and apply the concepts in the assignment. Keep this in mind while writing your paper.

Module 4 – Case

SAMPLING, HYPOTHESIS TESTING, AND REGRESSION

Case Assignment

By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results.

Choose one design method from the list below. Using your example, make a list of 2 or 3 advantages and 2 or 3 disadvantages for using the method. (2 pts)

Simple random sampling

Systematic sampling

Stratified sampling

Cluster sampling

The name of each student in a class is written on a separate card. The cards are placed in a bag. Three names are picked from the bag. Identify which type of sampling is used and why. (2 pts)

A phone company obtains an alphabetical list of names of homeowners in a city. They select every 25th person from the list until a sample of 100 is obtained. They then call these 100 people to advertise their services. Does this sampling plan result in a random sample? What type of sample is it? Explain. (2 pts)

The manager of a company wants to investigate job satisfaction among its employees. One morning after a meeting, she talks to all 25 employees who attended. Does this sampling plan result in a random sample? What type of sample is it? Explain. (2 pts)

An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects 10 schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? What type of sample is it? Explain. (2 pts)

Fifty-one sophomore, 42 junior, and 55 senior students are selected from classes with 516, 428, and 551 students respectively. Identify which type of sampling is used and explain your reasoning. (2 pts)

You want to investigate the workplace attitudes concerning new policies that were put into effect. You have funding and support to contact at most 100 people. Choose a design method and discuss the following:

Describe the sample design method you will use and why. (2 pts)

Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.? (2 pts)

Discuss the bias, on the part of both the researcher and participants. (2 pts)

A local newspaper wanted to gather information about house sales in the area. It distributed 25,000 electronic surveys to its readers asking questions about house sales in the past 6 months. Of the surveys sent out, 3.2% were returned. The results found that 92% of people did not sell their house in the past 6 months and 85% of people would expect a loss if they sold their house. The writer wants to use these results to conclude that the housing market is declining, and we are headed for a recession.

Explain the bias and sampling error in this study. (2 pts)

Should the writer conclude that the housing market is declining based upon this data? (2 pts)

Why or why not? (2 pts)

A homeowner is getting carpet installed. The installer is charging her for 250 square feet. She thinks this is more than the actual space being carpeted. She asks a second installer to measure the space to confirm her doubt. Write the null hypothesis Ho and the alternative hypothesis Ha. (2 pts)

Drug A is the usual treatment for depression in graduate students. Pfizer has a new drug, Drug B, that it thinks may be more effective. You have been hired to design the test program. As part of your project briefing, you decide to explain the logic of statistical testing to the people who are going to be working for you.

Write the research hypothesis and the null hypothesis. (2 pts)

Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II error. (2 pts)

Write a paragraph explaining which error would be more severe, and why. (2 pts)

Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variation from bottle to bottle. The amounts in the bottles are normally distributed with ? = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces):

5.95

6.10

5.98

6.01

6.25

5.85

5.91

6.05

5.88

5.91

Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle?

State the hypothesis you will test. (2 pts)

Calculate the test statistic. (2 pts)

Find the P-value. (2 pts)

What is the conclusion? (2 pts)

Calculate a Z score when X = 20, ? = 17, and ? = 3.4. (2 pts)

Using a standard normal probabilities table, interpret the results for the Z score in Problem 12. (2 pts)

Your babysitter claims that she is underpaid given the current market. Her hourly wage is $12 per hour. You do some research and discover that the average wage in your area is $14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not. (2 pts)

Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is ?=350 and ?=35. The 100 students who completed the tutoring program had an average score of 385 points.

Is the students’ average score of 385 points significant at the 5% and 1% levels to support Tutor O-Rama’s claim of at least a 50-point increase in the SAT score? (2 pts)

Is the Tutor O-Rama students’ average score of 385 points significantly different at the 5% and 1% levels from the average score of 350 points on the math portion of the SAT? What conclusion can you make, based on your results, about the effectiveness of Tutor O-Rama’s tutoring? (2 pts)

Module 4 – SLP

SAMPLING, HYPOTHESIS TESTING, AND REGRESSION

By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

In this assignment, you will continue to collect data for another 5–10 days. Write a paper (1–3 pages) including all of the following content:

Recalculate the mean, standard deviation, and variance.

Is your mean increasing or decreasing?

Explain the effects of the larger sample size in relation to your data.

Do you think the current sample you have is enough to draw an accurate conclusion, or do you need a larger sample?

What conclusions can you draw from comparing both sets of data?

Submit your paper at the end of Module 4.

SLP Assignment Expectations

Answer all questions posted in the instructions. Use information from the modular background readings and videos as well as any good-quality resource you can find. Cite all sources in APA style and include a reference list at the end of your paper.

Note about page length: Your ability to clearly articulate and explain these concepts is being assessed. The page length is a general guideline. A 3- or 4-page paper does not necessarily guarantee a grade of “A.” An “A” paper would include detailed information and explanations of all the assignment requirements listed above. The letter grade will be based upon demonstrated mastery of the content and ability to articulate and apply the concepts in the assignment. Keep this in mind while writing your paper.