# Assignment 2.1: Calculating Probability

**Note: followed by one response each Group (week two, week three, week four, week five.) discussions**

**Assignment 2.1: Calculating Probability**

Please provide solutions to the following problems. Please use Excel to solve the problems and submit the Excel spreadsheet.

1. A fair coin is tossed 15 times, calculate the probability of getting 0 heads or 15 heads

2. A biased coin with probability of head being .6 is tossed 12 times. What is the probability that number of head would more than 4 but less than or equal to 10.

3. You have a biased dice (with six faces numbered 1,2,3,4,5 and 6) in that odd numbers are thrice as likely as even numbers to show. You toss the dice 10 times. What is the probability that an even number would show up 5 times.

4. If z has a standard normal distribution, calculate the following probability. P(-.3≤z≤10)

5. If x has a normal distribution with mean 15 and standard deviation 2, calculate the following probabilities: P(1≤x<15)

**Week Two Group Discussion**

**Prompt:**

You have a biased dice (with six faces numbered 1,2,3,4,5 and 6) in that even numbers are twice as likely as odd numbers to show. You toss the dice 15 times. What is the probability that

1. An even number would show up 5 times?

2. 1 would show up five times?

1. Can it be formulated as a Binomial distribution for answering (a)? If so, how would you solve it?

2. Can it be formulated as a Binomial distribution for answering (b)? If so, how would you solve it?

**Assignment 3.1: Hypothesis Testing and Confidence Intervals**

Please provide solutions to the following problems. Please use Excel to solve the problems and submit the Excel spreadsheet.

1. Your average weekly grocery bill at the store you usually shop is $300. You decided to test a new strategy of buying most items over the weekend from Costco in bulk and when you fall short of some items during the week or the once not appropriate for Costco, you buy from a convenience store near you. You took a sample of your expenses for 20 weeks and found that the average is $285 and the standard deviation for the sample is $25. Set up your null and alternative hypothesis for testing whether your cists are different and do the analysis using α=.05.

2. You started a new restaurant. Based on invoices for the first 30 days, you estimated your average grocery bill to be $20,000 with a standard deviation of $2000. You want to start another restaurant in a similar neighborhood and you are planning to prepare a brochure for investors and to work out a deal with a whole sale food distributor. Prepare a 95% confidence interval for the average grocery bill. Would a 99% confidence interval be narrower or wider than the 95% confidence interval?

3. You move to a new town and want to decide on when to start for work. You do not want to reach too early and not be too late too many times. You, thus, collected data for 10 days and obtained an average of 34.5 minutes. You took the standard deviation of 4.5 minutes from a commuting friend and believe that that is the standard deviation for the area. Prepare a 95% confidence interval for the true average commuting time.

**Week Three Group Discussion**

**Prompt:**

In week 2 you participated in an activity that involved identifying your height and gender. Please review the final data from the activity shared in your google documents to answer the following discussion questions.

Testing the following:

1. Is the height of men in the eMBA class greater than the average height of men in the US?

2. Is the height of women in the eMBA class greater than the average height of women in the US?

3. Is the height of men in the eMBA class different than the average height of men in the US?

4. Is the height of women in the eMBA class different than the average height of women in the US?

Please ensure that you are centering your discussion around the following steps:

1. Setting up the hypotheses.

2. Obtaining average heights from the US Census Bureau website.

3. Gathering data (may be through survey tool on Blackboard). Also, ask if students trust that information would be anonymous. If not, obtain another approach for gathering data.

4. Test the hypothesis.

## Week Four Group Discussion

**Prompt:**

Please use the following information on Rating of Professor, Easiness of the course and whether students consider the professor to be hot or not. Regress Rating on Easiness and Hot and interpret the output, i.e., interpret correlation coefficient, F and t statistics for the model and individual estimates provided here.

How can you use this analysis?

**Assignment 4.1: Regression Analysis**

Please provide solutions to the following problems. Please use Excel to solve the problems and submit the Excel spreadsheet.

1. A group of student’s student gathered following information from web sites of few universities. Regress salary offers on their annual tuition and median GMAT score of students admitted to those programs and interpret these results.

__Salary and GMAT scores excel document__

**Week Five Group Discussion 5.1**

**Prompt:**

You have been contributing to the discussion on ethics and statistics throughout the course. Take a moment to make a final post and comments answering these questions:

· Think about the research that you did with your team for your final report and presentation. Do you think your personal values or biases affected certain aspects of your research and interpretation of statistics? How so?

· Do some research online and share an example of how a company/organization may have used statistical analysis unethically. What might have led them to do so?

## · Week Five Group Discussion 5.2

· **Prompt:**

· While exploring MBA programs, a student gathered the following information. What kind of relationship exists between variables and how can this information be used in decision making (i.e. what data would you gather on other schools as you continue your search).

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