Two dice are thrown.

Let A be the event that an odd number is obtained on the first dice, B be the event that the number obtained is greater than 5 on the first dice, C be the event that the number obtained on the second dice is smaller than 5, and D be the event that the sum of the two numbers obtained is 8.

State whether each of the following is a pair of independent events or dependent events.

(a) A and B

(b) A and C

(c) B and D

(d) C and D

1. For a Normal distribution N (μ, σ), if we know the population standard deviation then we can make an inference about:

1. Mode

2. Range

3. Mean

4. Median

2. The Normal Distribution curve of heights of a large population of people indicates that the mean height (μ) of the population is 5 feet 6 inches. The 1 standard deviation (σ) in height variation is 2 inches. The people who have the heights between 5 feet 2 inches and 5 feet 10 inches represent:

   1. the range of +1σ to -1 σ

   2. the range of +2σ to -2 σ

   3. the range of +3σ to -3 σ

3. The Normal Distribution curve of heights of a large population of people indicates that the mean height (μ) of the population is 5 feet 3 inches. The 1 standard deviation (σ) in height variation is 2 inches. The people who have the heights between 4 feet 11 inches and 5 feet 7 inches represent:

   1. the range of +2σ to -2 σ

   2. the range of +σ to -σ

   3. the range of +3σ to -3 σ

20. The Normal Distribution curve of heights of a large population of people indicates that the mean height (μ) of the population is 5 feet 5 inches. The 1 standard deviation (σ) in height variation is 2 inches. The people who have the heights between 5 feet 3 inches and 5 feet 7 inches represent:

    1. the range of +2σ to -2 σ

    2. the range of +σ to -σ

    3. the range of +3σ to -3 σ

CENTRAL LIMIT THEOREM (Sampling Distribution)

28. According to the Central Limit Theorem , as the SRS increases, that is as n INCREASES, the sample mean is

1. Closer to the population mean µ

2. Away from the population mean µ

29. According to the Central Limit Theorem, as the SRS increases, that is as n INCREASES, the sample distribution becomes

1. Left-skewed distribution

2. Right-skewed distribution

3. Normal Distribution

A random survey test was given to 100 students. The average score (mean) x was 75. The standard deviation, σ, was 20. Answer the following questions based on this information. Note: n = 100 and look at PPT on Confidence Interval posted on BB.

30. The ‘Law of Large Numbers’ states that as no. of observations drawn INCREASES, the observed mean gets closer to the

1. Standard deviation of the population

2. Probability of the population

3. Mean of the population

31. The standard deviation of a Normal Distribution of IQ of a population of adults is 15. For a simple random size (SRS) of 9 from this population, the standard deviation for the sampling distribution will be:

1. 15

2. 15/9

3. 9

4. 5

32. The 95%-confidence interval means that we got these numbers using a method that gives CORRECT results …… of the times.

1. 68%

2. 100%

3. 99.7%

4. 95%

33. The 95%-confidence interval means that the MARGIN OF ERROR is only:

1. 95%

2. 5%

3. 68%

4. 99.7%

34. The margin of error for a sample of n =1000 will be ……. for a sample of n =50.

1. Less than

2. Greater than

3. Equal to

35. For a sample size of ‘N’ the degrees of freedom for some statistical tests can be computed from the formula:

1. N-5

2. N-2

3. N-3

4. N-4

HYPOTHESIS TESTING (Read the chapter and you will find the answers)

36. A Hypothesis always refers to a …….of population.

1. Mean

2. Standard deviation

37. The hypothesis that “The more beer you drink…the higher your blood alcohol level will be” an example of:

    1. Null Hypothesis

    2. Alternative Hypothesis

38. The value of α = 0.05 means that we are requiring that data give evidence AGAINST the Null Hypothesis so strong that it would happen ……… of the time.

1. No more than 95%

2. No less than 95%

3. No more than 5%

4. No less than 50%

Learning Objective: The final statistics project will provide you with the opportunity to demonstrate your understanding of the applied aspect of this course. In fulfilling this objective, you will fulfill the written statistical component requirement of the BBA program. You will decide on two valuable options. Option 1 will focus on making your own mini statistical study.

OPTION 1 First, brainstorm a problem (e.g., health, debt, student success, work, stress, happiness, customer satisfaction, etc.) that you're interested. It can be anything relevant to business, economics, management, etc.

Second, at least two different research questions and/or hypotheses. Note: The null and the alternative hypotheses count as ONE hypothesis. You need TWO different hypotheses/research questions. Sample question: Do students that drink energy drinks have higher GPAs? (Correlation)

Sample question: Do women experience more conflict at work than do men? (Independent Sample T-Test)

Sample question: Are there differences in degree choice satisfaction among freshman, sophomore, juniors, and seniors? (ANOVA)

Sample research hypothesis: H1: Men and women differ in their workplace stress levels. (Independent Sample T-Test)

Sample research hypothesis: H1: Drinking coffee impacts students' scores on exams. (Simple Linear Regression)

Sample research hypothesis: H1: Watching the news too often is correlated with being pessimistic about the world. (Correlations)

Third, develop at least a 5-10 question survey relevant to the research question or research hypothesis of your choice.

Sample survey questions. i. What's your sex? Male (1) ____ Female (2) ___ ii.

What is your age? ____ iii.

Have you ever experienced workplace conflict? Yes (1)___ No (0) ____ iv.

On a scale of 1-7, how stressed are you at work? Not stressed out 1 2 3 4 5 6 7 Very stressed out v.

How many times do you watch the news per week? ____ vi.

Do you experience stress due to conflict? Yes (1) ___ No (0) ___

vii. What is your perception of the current political leaders in the U.S.?

Fourth, collect the data from at least 10+ different people. (online or face-to-face) a a free online survey software system like Qualtrics or SurveyMonkey. Share the public hyperlink to at least 10 people (your target audience) through texts, social networking sites, emails, etc.... Then, download the responses as an Excel spreadsheet.

Fifth, select an analytical approach as a key word (e.g., percentages, frequencies, means, standard deviations, t-tests, ANOVA, linear regression, regression analysis, correlational analysis, multiple regression, etc...). Select the approaches according to your personal research question/hypothesis interests.

Sixth, design two visual graphical displays of the data (e.g., pie chart, bar graph, histogram, etc.) and/or analyze the data (e.g., correlation, t-test, ANOVA, regression) to share.

Seventh, interpret the results of your mini study. What's the answer to your questions and/or hypotheses? Share the visual results in your statistical report.

Eighth, find two credible references that support your study to enhance the professionalism and the credibility of your study. Make sure to cite them in your managerial report.

Ninth, complete the managerial report worksheet to help you draft your final managerial report.

Discuss the Data that was Selected and Where you got it from:

What data were selected? Why is this data interesting to you? Why is this issue important?

What data set was selected and why? What was the target audience who responded to the data set?

Overview the report

Hypotheses or Research Questions:

What were at least two hypotheses or research questions posed by the researcher(s)?

Methods:

What was the sample size? Any descriptive information?

What was the methodology employed in this study (e.g., surveys, interviews)? Was it adequate?

Analysis:

What data analysis strategies were adopted (e.g., descriptive (percentages, frequencies, means), t-test, ANOVA, linear regression, correlation, multiple regression)

Results:

Where each of the hypothesis (or research questions) supported or not supported given the selected data set?

Explain the findings using your own words.

*You must integrate at least two graphs/tables in your managerial report*

Conclusion:

Summarize your results

Conclude the report with a quote, or with a startling comment.

A consignment of 12 car engines contains 1 engine that is faulty. Two engines are chosen randomly from this consignment for testing. How many different combinations of 2 engines can be chosen?

From a standard 52 card deck, how many 6 card hands contain:

(a) three (different) pairs

(b) a five card straight and a pair (a straight can only begin with A, 2, 3, ..., 10)

(c) only a high card (ie. no pair, no five card straight, no five card flush)

Please answer all parts of the question with explanation

Scenario 4

A warehouse has a new leadership team and they wanted to prove their performance was as good or better than the previous leadership team. They measured on-time shipping and accurate order fulfillment. Their data showed a correlation value of 0.70 and a regression value of 0.49 between on-time shipping and accurate order fulfillment. The previous leadership teams’ corresponding numbers for on-time shipping and accurate order fulfillment were a correlation value of 0.80 and a regression value of 0.64.

1. What conclusions can you summarize from these numbers in plain English?

2. Based on this data what future course of action do you recommend for your client?

Scenario 5

The same warehouse leadership team in Scenario 4 measured damaged products and warehouse capacity. Their data showed a correlation value of -0.50 and a regression value of 0.25 between damaged products and warehouse capacity.

1. What conclusions can you summarize from these numbers in plain English?

2. Based on this data what future course of action do you recommend for your client?

4. Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table)

a. Construct the 95% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Confidence interval is to .

b. Specify the competing hypotheses in order to determine whether or not the population means differ.

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

c. Using the confidence interval from part a, can you reject the null hypothesis?

• Yes, since the confidence interval includes the hypothesized value of 0.

• No, since the confidence interval includes the hypothesized value of 0.

• Yes, since the confidence interval does not include the hypothesized value of 0.

• No, since the confidence interval does not include the hypothesized value of 0.

d. Interpret the results at αα = 0.05.

• We conclude that population mean 1 is greater than population mean 2.

• We cannot conclude that population mean 1 is greater than population mean 2.

• We conclude that the population means differ.

• We cannot conclude that the population means differ.

Please explain how the proportions for two populations are used in hypotheses testing about two population proportions. Please give an example.

A simple random sample was taken of 1000 shoppers Respondents were classified by gender (male or female) and by meat department preference (beef, chicken, fish). Results are shown in the contingency table:

Is there a difference in meat preference between males and females? The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. Use a 0.05 level of significance.  

Χ² = (200 - 180)²/180 + (150 - 180)²/180 + (50 - 40)²/40
    + (250 - 270)²/270 + (300 - 270)²/270 + (50 - 60)²/60
Χ² = 400/180 + 900/180 + 100/40 + 400/270 + 900/270 + 100/60
Χ² = 2.22 + 5.00 + 2.50 + 1.48 + 3.33 + 1.67 = 16.2

As you can see, the math gets a bit cumbersome, so I did it for you!  

a & b) State the null and alternative hypotheses: Ho ___?___ , Ha ___?___

c. Which specific type of chi square test was used for this analysis? ___?___

d. What are the degrees of freedom used for this problem (columns -1)(rows -1) = df = ___?___

e. So, the P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than (enter a value) ___?___

The P-value was calculated for you: P(Χ2 > 16.2) = 0.0003

f. Based on the given information, interpret the results in symbols and values ________

g. Then interpret the results in words (full sentence) ___________

h. What will the distribution look like on a Bell curve? ____________

The number of pig farms is increasing, a study was conducted to test if composted pig manure might be a better fertilizer than composted cow manure. Eight corn fields of equal size were chosen for the experiment. One half of each corn field was fertilized with composted cow manure and the other half was fertilized with composed pig manure. The yields are given in the following table.

Test at a = 0.01 the claim that the average yield is higher for composted pig manure than it is for composted cow manure.

Some critics of big business argue that CEOs are overpaid and that their compensation is not related the performance of their company. To test this theory, data on executive's total pay and company's performance was collected from a randomly selected set of fifty companies.

A. Identify the independent variable(s) - If any (and define them precisely and indicate whether they are qualitative or quantitative).

B. Identify the dependent variable - if any (and define them precisely and indicate whether they are qualitative or quantitative).

C. Identify the type of analysis that is appropriate (Chi- Square test of independence, ANOVA, Regression, or Correlation)

D. Justify why the analysis you identified in part C is correct.

a. What is hypothesis testing in statistics? Discuss

b. Does Type I error being considered more serious than Type II error? Explain

c. What is the p-value of a test? Give an example

Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give the best point estimate for μ, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed.

A 95% confidence interval for μ using the sample results x= 94.6, s= 6.9, and n =42

Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places.

point estimate =

margin of error =

the 95% confidence interval =

Read the following description and then answer items 12 to 16: Researchers are interested in determining if there is a difference between two exercise regimens (A and B). The researchers think that the regimens may have differential effects on a treadmill test where the participants run to exhaustion.

12.Write the appropriate null hypothesis.

14. What is the dependent variable in this study?

16. Describe what happens if the researchers make a type II error.

Consider a manufacturing process that produces cylindrical component parts for the automotive industry. According to specifications, it is important that the process produces parts having a mean diameter of 5.0 millimeters. An experiment is conducted in which 100 parts produced by the process are selected randomly and the diameter measured on each part. It is known that the population standard deviation is 0.1. It was found that the sample mean diameter is 5.027 millimeters. The process engineer Mr. Tan would like to find out how likely is it that one could obtain a sample mean diameter of at least 5.027 with sample size n = 100, if the population mean µ = 5.0. Apply the concept of central limit theorem. Mr Tan claimed that “In only 7 in 1000 experiments, one would experience by chance a sample mean that deviates from the population mean by as much as 0.027.” Do you agree? Explain your reasoning.