Q-3: A nation job placement company is interested in developing a model that might be used to explain the variation in starting salaries for college graduates based on the college GPA. The following data were collected through a random sample of the clients with which this company has been associated. Starting Salary GPA 3.20 3.40 2.90 3.60 2.80 2.50 3.00 3.60 2.90 3.50 $35,000 $29,500 $30,000 $36,400 $31,500 $29,000 $33,200 $37,600 $32,000 $36,000 Based on this sample information: (a). Calculate the correlation coefficient between these two variables. (b). Conduct a test of hypothesis to determine if there exists a correlation between the two variables in the population. Use a significance level of 0.05. (c). determine the least squares regression model. Also, develop a scatter plot of the data and locate the regression line on the scatter plot.

The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.  Car Age (years) Selling Price ($000) 1 11 12.1 2 8 10.5 3 14 5.7 4 17 4.9 5 9 5.0 6 8 13.4 7 10 10.5 8 14 9.0 9 13 9.0 10 17 4.5 11 6 12.5 12 6 11.5   Click here for the Excel Data Filea. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) a= b=   Estimate the selling price of an 7-year-old car (in $000). (Round your answer to 3 decimal places.) Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount.)

The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" stocks or bargain stocks. A random sample of 51 of the largest companies in the United States gave the following P/E ratiost. 9 20 11 35 19 13 15 21 29 53 16 26 21 14 21 27 10 12 47 14 40 18 60 72 33 14 8 49 5 16 8 19 12 31 67 51 26 18 17 20 19 13 25 23 27 44 20 27 19 18 32 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.) (b) Find a 90% confidence interval for the P/E population mean u of all large U.S. companies. (Round your answers to one decimal place.) lower limit upper limit (c) Find a 99% confidence interval for the P/E population mean u of all large U.S. companies. (Round your answers to one decimal place.) lower limit upper…

When an audit must be conducted that involves a tedious examination of a large inventory, the audit may be very costly and time consuming if each item in the inventory must be examined. In such situations, the auditor frequently obtains a random sample of items from the complete inventory and uses the results of an audit of the sampled items to check the validity of the company's financial statement. A large company’s financial statement claims an inventory that averages $600 per item. The following data are the auditor’s assessment of a random sample of 75 items from the company’s inventory. The values resulting from the audit are rounded to the nearest dollar. Estimate the mean value of an item in the inventory using a 95% confidence interval. Is there substantial evidence (a 5 .01) that the mean value of an item in the inventory is less than $600? What is the target population for the above inferences? Would normal distribution–based procedures be appropriate for answering the…