1. Company XYZ is in the process of evaluating whether it should move to internet sales because a marketing research manager believes that, on average, each internet sale is at least $20 more than a similar sale in stores. If the marketing research manager is right, the company would like to move to internet sales. The company's competitor only offers internet sales, and their average order (based on a sample of 50 orders) is $52 with a variance of $25. Of XYZ's 50 in-store sales orders, the average sale was $30 with a variance of $16. Based on the p-value test and alpha=0.05, what would you advise the company

1.Suppose you are tasked with analyzing productivity data for a firm that produces outsourced reports for other companies. The first few rows of the data look like this, where reports is the number of reports produced in an observed week, num_employees is the number of employees who worked that week and total_employee_hours is the number of combined hours worked by those employees that week:

reports

num_employees

total_employee_hours

1441

19

543

1517

16

524

1385

12

505

1518

11

521

2209

19

720

1384

11

549

...

...

...

We run a regression on the full dataset and obtain the following output:

a.Based on the regression output, how many weeks of data are in our full sample, and how much of the variation in the number of reports produced is explained by the two independent variables (please specify what value you use to estimate the amount of variation explained)? (2 points)

b.What is the equation for this regression model that we would use to produce a point estimate for number of reports produced in a given week in the future? (2 points)e equal, if we were to add one more employee working an additional 40 hours that week. [3 points]

1. c.Use the coefficients to predict a point estimate of how many additional reports we would expect to produce, all els

1.Suppose we know that, historically, the standard deviation of annual rainfall in a particular state is 2 inches. (8 points total)

a.We measure rainfall in that area for 35 years, and we find an average of 37 inches per year. What is the 95% confidence interval for the average rainfall? [5 points]

b.How many years of data would we need if we want to estimate the actual average within less than plus-or-minus 0.5 inches at 95% confidence? [3 points]