Paired t test

Use the five-step hypothesis testingprocedure to solve the following exercises.

1.) State the null hypothesis and the alternate hypothesis.
2.) What is the critical value of t?
3.) What is the computed value of t?
4.) Interpret the result. What is the p-value?
5.) What assumption needs to be made about the distribution of the differences?

To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded. The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople.

Salesperson Before After
Sid Mahone $320 $340
Carol Quick 290 285
Tom Jackson 421 475
Andy Jones 510 510
Jean Sloan 210 210
Jack Walker 402 500
Peg Mancuso 625 631
Anita Loma 560 560
John Cuso 360 365
Carl Utz 431 431
A. S. Kushner 506 525
Fern Lawton 505 619

Was there a significant increase in the typical salesperson’s weekly income due to the innovative incentive plan? Use the .05 significance level. Estimate the p-value, and interpret it.

Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.