The statistics department is interested in the different factors that might influence a student’s score on the final exam. They identify three factors to test: the student’s midterm exam score, the number of hours the student reports having studied for the final exam, and the average number of drinks of alcohol the student reports having on a night out. They collect data on all of these factors and want to estimate the following model:

FinalExamScore=β0+β1 MidtermExamScore +β2HourStudied +β3AverageAlcohol +ε

Variable Descriptions:

Final Exam Score: A student’s final exam score, measured in % on scale from 0 – 100

Midterm Exam Score: A student’s midterm exam score, measured in % on scale from 0 – 100

Hour Studied: The number of hours the student reports studying for the final exam

Average Alcohol: The average number of alcoholic drinks the student reports having on a typical night out.

For this question, you will need to download the Student Grade Data and then use the data analysis tool pack in Excel to run a regression. Note, you will need to install the data analysis tool pack on your computer. How to do this differs based on the type of computer you are using, but instructions can be found on google for both Mac and PC.

https://arizona.grtep.com/core/uploadfiles/components/282918/files/Student%20Grade%20Data.xlsx (Student Grade Data)

Estimate the sample regression equation above and fill in the estimated coefficients. Round the coefficient estimates to 4 decimals.

FinalExamˆScore=_______+_______MidtermExamScore+_____HourStudied−______AverageAlcohol

Predict a student’s final exam score who scored a 79% on the midterm, studied for 15 hours, and who only drinks 2 drinks on an average night out. Round your answer to 2 decimals. Hint, be sure to use your coefficients that were rounded to 4 decimal points.

As part of an investment firm, you have been asked to research potential companies for the firm to invest in. Specifically, you are interested are interested in identifying the factors that influence a company’s earnings before taxes. You hypothesize that a firm’s current assets, current liabilities, and amount the firm pays in interest on its loans all might play a role in predicting a company’s earnings before taxes. Therefore, you collect data on all of the variables from several different companies.

Use this data to estimate the following model and answer each of the questions below.

EBT= β0+β1TotAssets+ β2 TotLiabilities+ β3 InterestExpense +ε

Variable Descriptions:

EBT: A firm’s total reported earnings before taxes measured in millions of dollars

Tot Assets: A firm’s total current assets measured in millions of dollars

Tot Liabilities: A firm’s total current liabilities measured in millions of dollars

Interest Expense: A firm’s total expense on interest paid on loans measured in millions of dollars

For this question, you will need to download the Stock Data and then use the data analysis tool pack in Excel to run a regression. Note, you will need to install the data analysis tool pack on your computer. How to do this differs based on the type of computer you are using, but instructions can be found on google for both Mac and PC. Estimate the sample regression equation above and fill in the estimated coefficients. Round the coefficient estimates to 4 decimals.

https://arizona.grtep.com/core/uploadfiles/components/282919/files/Stock%20Data.xlsx (Stock Data)

EBTˆ=_____+_____TotAssets+____TotLiabilities+____InterestExpense

Predict the earnings before taxes for a company with 1.5 billion dollars in assets, 900 million dollars in liabilities, and 80 million dollars in interest expenses. Make sure to use the rounded coefficients when making the prediction. Round your final answer to 4 decimals. Hint, make sure you pay attention to the units!

The weights of 3 randomly selected mattresses were found to have a standard deviation of 4.53. Construct the 95% confidence interval for the population standard deviation of the weights of all mattresses in this factory. Round your answers to two decimal places.

Find the Lower Endpoint and Upper Endpoint

Solve the question and show all steps: Consider the probability distribution shown here:

a. Calculate E(Y) or µ, VAR(Y) or ? 2 , and STDV(Y) or σ

b. Graph P(Y). Locate µ, µ - 2σ, and µ + 2σ on the graph

c. What is the probability that Y is in the interval ? ± 2??

Perform the appropriate hypothesis test for the problem. State the hypotheses, identify the claim, compute the test statistic and P-value, make a decision, and write the interpretation in terms of the claim. For consistency, use a significance level of 0.05 for the problem.

Two brands of components are installed in a random sample of machines and the total machine operation time (in minutes) until the component needs to be replaced is recorded. Can you conclude that Brand 1 has a better mean lifetime based on the data below?

A radar unit is used to measure the speed of cars on a highway during rush hour traffic. The speeds of individual cars are normally distributed with a mean of 55 mph and a standard deviation of 3.2 mph. Find the probability of the following events:
(a) A car traveling faster than average.
(b) A car traveling over 65 mph
(c) A car traveling between 48 and 50 mph.

CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8.5 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting time differs from this standard.

1. Formulate the hypotheses for this application.

Ho:u=8.5

Ho:=/8.5

3. A sample of 100 shoppers showed a sample mean waiting time of 8.6 minutes. Assume a population standard deviation of  o=3.8 minutes. What is the p-value?

z values =? To 2 decimals

p-value=? To 4 decimals

d. Compute a 98% confidence interval for the population mean. Does it support your conclusion?

  ,   (to 2 decimals)

1. Thoroughly describe independent and dependent variables in complete sentences.

2. Thoroughly describe why you think they are related in complete sentences.

A fair 6-sided die is rolled repeatedly. (a) Find the expected number of rolls needed to get a 1 followed right away by a 2. Hint: Start by conditioning on whether or not the first roll is a 1. (b) Find the expected number of rolls needed to get two consecutive 1’s. (c) Let an be the expected number of rolls needed to get the same value n times in a row (i.e., to obtain a streak of n consecutive j’s for some not-specified-in-advance value of j). Find a recursive formula for an+1 in terms of an. Hint: Divide the time until there are n+1 consecutive appearances of the same value into two pieces: the time until there are n consecutive appearances, and the rest. (d) Find a simple, explicit formula for an for all n ≥ 1. What is a7 (numerically)?

1. Thoroughly describe independent and dependent variables in complete sentences.

2. Thoroughly describe why you think they are related in complete sentences.

Locate the results of a recent survey that shows at least two variables in a newspaper, magazine, or internet article. Outline the survey data so that your peers can understand the variables and results, and then identify at least one key formula that you could use to evaluate the data. Provide a brief explanation of why you selected the formula you did and why it matters.

A cell with a radius of 1 µm has an exponential growth rate of 0.5 d-1, based upon assimilation of glucose. A cell with a very similar genome and metabolism and a radius of 100 µm is growing in the same habitat. If growth rate of both cells is limited by glucose uptake rate, predict the growth rate of the larger cell.

Collect data on one response (dependent or y) variable and two different explanatory (independent or x) variables. This will require a survey with three questions. For example: To predict a student’s GPA (y), you might collect data on two x variables: SAT score and age. So we would be trying to determine if there was a linear correlation between someone’s SAT score and their GPA, as well as their age and their GPA. (Note: students may not choose GPA as their dependent variable, must pick a different topic.)

• This data must be quantitative, not qualitative.

• Collect data from at least 15 people. Each person must answer all three questions for their data to count.

• Prepare a brief report that shares the questions used, as to why they are important to be studied.

• Present data in table form and as a scatter plot. You can create your tables and graphs in Excel, but they will need to be copy and pasted into your Word document. Do NOT submit an Excel file as it will not be graded.

• Model the data with two linear regressions (one for each x & y pair.)

• Interpret each linear model.

• Use each of your models to make a prediction.

Homework 4: Probability and z scores

14. Use the data to answer the following questions
14. Show all work (*round 2 decimals places)

• What is the mean & SD for the distribution of scores?
• What is the corresponding z score for each raw score?
• What is the probability of getting a raw score greater than 4?
• What is the probability of getting a raw score less than 2?
• What is the probability of a raw score between 4 & 6?
• What is the probability of a raw score between 3 & 6?