Two events ?1 and ?2 are defined on the same probability space such that: ?(?1 ) = 0.7 , ?(?2 ) = 0.5 , and ?(?1 ??? ?2 ) = 0.3. a) Find ?(?1 ?? ?2 ). b) Find ?(?1 | ?2 ). c) Are ?1 and ?2 mutually exclusive (disjoint)? and why? d) Are ?1 and ?2 independent? and why?

The frequency of carriers for a rare autosomal recessive genetic condition is 0.04 in a population. Assuming this population is in Hardy-Weinberg equilibrium, what is the allele frequency of the recessive allele?

This case is based on an actual situation. Centennial Construction Company, headquartered in Dallas, Texas, built a Rodeway Motel 35 miles north of Dallas. The construction foreman, whose name was Slim Chance, hired the 40 workers needed to complete the project. Slim had the construction workers fill out the necessary tax forms, and he sent their documents to the home office.Work on the motel began on April 1 and ended September 1. Each week, Slim filled out a timecard of hours worked by each employee during the week. Slim faxed the timecards to the home office, which prepared the payroll checks on Friday morning. Slim drove to the home office on Friday, picked up the payroll checks, and returned to the construction site. At 5 p.m. on Friday, Slim distributed payroll checks to the workers.Requirements1. Describe in detail the main internal control weakness in this situation. Specify what negative result(s) could occur because of the internal control weakness.

The data below is the mileage (thousands of miles) and age of your cars .

Year Miles Age

2017    8.5    1

2009 100.3    9

2014   32.7    4

2004 125.0   14

2003 115.0   15

2011   85.5    7

2012   23.1    6

2012   45.0    6

2004 123.0   14

2013   51.2    5

2013 116.0    5

2009 110.0    9

2003 143.0   15

2017   12.0    1

2005 180.0   13

2008 270.0   10

Please include appropriate Minitab Results when important

a. Identify terms in the simple linear regression population model in this context.

b. Obtain a scatter diagram for the sample data. Interpret the scatter diagram.

c. Obtain a scatter diagram with the least squares regression line included. Interpret the intercept and slope in the context of this problem.

d. In theory what ought to be the value of the population model intercept? Explain.

e. What is the informal prediction for what the mileage should be on your car? What is the error in the prediction of the mileage for your car?

f .Use some statistical reasoning to assess whether or not the prediction for the mileage on your car was “accurate”?

g. How would you respond if someone asks “about” how many miles do students drive per year?

The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Independent simple random samples for both Buffalo and Boston are located in the Excel Online file below. Construct a spreadsheet to answer the following questions.

Open spreadsheet

Round your answers to one decimal place.

1. What is the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day?

2. What is the 95% confidence interval for the difference between the two population means?

1. It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 36 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 114 feet. Assume that the population standard deviation is 22 feet.

a. Set up the null and the alternative hypotheses for the test.

b. Calculate the value of the test statistic.

c. Find the p-value.

d. Calculate the critical value using α = 0.01

e. Use α = 0.01 to determine if the average breaking distance differs from 120 feet.

2. Consider the following hypotheses:
H₀: μ ≤ 12.6
H_A: μ > 12.6
A sample of 25 observations yields a sample mean of 13.4. Assume that the sample is drawn from a normal population with a population standard deviation of 3.2.

a. Calculate the value of the test statistic.

b. Find the p-value.

c. Calculate the critical value using α = 0.05

d. What is the conclusion if α = 0.05? Interpret the results at α = 0.05.

e. Calculate the p-value if the above sample mean was based on a sample of 100 observations.

f. Based on a sample of 100 observations, what is the conclusion if α = 0.10? Interpret the results at α = 0.10.

The data below is the mileage (thousands of miles) and age of your cars as sample.

Year Miles Age

2017    8.5    1

2009 100.3    9

2014   32.7    4

2004 125.0   14

2003 115.0   15

2011   85.5    7

2012   23.1    6

2012   45.0    6

2004 123.0   14

2013   51.2    5

2013 116.0    5

2009 110.0    9

2003 143.0   15

2017   12.0    1

2005 180.0   13

2008 270.0   10

Please include appropriate Minitab Results when important

a. Identify terms in the simple linear regression population model in this context.

b. Obtain a scatter diagram for the sample data. Interpret the scatter diagram.

c. Obtain a scatter diagram with the least squares regression line included. Interpret the intercept and slope in the context of this problem.

d. In theory what ought to be the value of the population model intercept? Explain.

e. What is the informal prediction for what the mileage should be on your car? What is the error in the prediction of the mileage for your car?

f. Use some statistical reasoning to assess whether or not the prediction for the mileage on your car was “accurate”?

g. How would you respond if someone asks “about” how many miles do students drive per year?

The data below is the mileage (thousands of miles) and age of your cars .

Year Miles Age

2017    8.5    1

2009 100.3    9

2014   32.7    4

2004 125.0   14

2003 115.0   15

2011   85.5    7

2012   23.1    6

2012   45.0    6

2004 123.0   14

2013   51.2    5

2013 116.0    5

2009 110.0    9

2003 143.0   15

2017   12.0    1

2005 180.0   13

2008 270.0   10

Please include appropriate Minitab Results when important

a. Identify terms in the simple linear regression population model in this context.

b. Obtain a scatter diagram for the sample data. Interpret the scatter diagram.

c. Obtain a scatter diagram with the least squares regression line included. Interpret the intercept and slope in the context of this problem.

d. In theory what ought to be the value of the population model intercept? Explain.

e. What is the informal prediction for what the mileage should be on your car? What is the error in the prediction of the mileage for your car?

f .Use some statistical reasoning to assess whether or not the prediction for the mileage on your car was “accurate”?

g. How would you respond if someone asks “about” how many miles do students drive per year?