# Paired t test

Use the five-step hypothesis testing procedure 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.

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#### Solution Summary

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.