TAE 8 Conduct an investigation taking into consideration the following concepts: * Include numerical examples with your formulas and hypotheses for a better understanding of the definitions....

Homework


TAE 8 Conduct an investigation taking into consideration the following concepts: * Include numerical examples with your formulas and hypotheses for a better understanding of the definitions. Determination coefficient Standard error of estimation Dependent variable Independent variable Regression line Guiding questions to answer in writing: Explain the assumptions of the simple linear regression model. Explain the usefulness of the scatter plot as a possible starting point for developing a bivariate linear regression model. Explain what the standard error of estimate measures in the simple linear regression model. What role does the coefficient of determination play? Second part 1) A sample of 12 houses that were sold last week in San Juan is selected. Can you conclude that as the size of the house increases (reported in the following table in thousands of square feet), so does the sale price (reported in thousands of dollars)? House size (thousands of square feet) Sale price (thousands of dollars) House size (thousands of square feet) Sale price (thousands of dollars) 1.4 100 1.3 110 1.3 110 0.8 85 1.2 105 1.2 105 1.1 120 0.9 75 1.4 80 1.1 70 1.0 105 1.1 95 1. Calculate the correlation coefficient 2. Calculate the coefficient of determination 3. Determine the regression equation 4. Is there a positive association between the size of the home and its sale price? Use the 0.05 level of significance. 2) A research company conducted a survey to determine the average amount that smokers spend on cigarettes during a week. The company found that the distribution of amounts they spend per week tended to follow a normal distribution, with a standard deviation of $ 5. A sample of 49 smokers revealed that the median expense is $ 20. What is the probability that the sample mean is greater than $ 22? 3) You need to calculate an interval of the average ages of adults of voting age in an electoral district, for this you obtain a random sample of 272 adults of voting age and determine a mean age of 36.3 years with a standard deviation of 9.7 years . Create a 90% confidence interval and explain your result. 4) A restaurant chain claims that the customer wait time is 8 minutes with a population standard deviation of 1 minute. The quality control department found in a sample of 49 clients that the average waiting time was 2.75 minutes. With the 0.05 level of significance, can you conclude that the mean waiting time is greater than 3 minutes? Demonstrate the procedure and explain your answer. Consider the following when submitting your test: • Justify any assumptions made to solve the exercises. • Use the APA style manual when submitting your proof in MS Word document.