# Statistic problems – The null and alternate hypothesis

#1

The null and alternate hypothesis:

Null hypothesis : (MU)population mean^1 = (MU) population mean^2

Alternate hypothesis: (MU)population mean^1/=(MU) population mean^2

A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample deviation of 15. At the .10 significance level is there a difference in population mean?

#2

Ms. Lisa Monnin is the budget director for Nexus Media, Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.

Sales(\$) 131 135 146 165 136 142

Audit(\$) 130 102 129 143 149 120 139

At the .10 significance level can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value?

#3

Use the five-step hypothesis to solve the following exercise:

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

Sales person Before After

Sid Mahone \$320 \$340
Carol Quick 290 285
Tom Jackson 421 475
Andy Johnson 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 significance increase in the typical salespersons weekly income due to innovative incentive plan? Use the 0.5 significance level. Estimate the p-value and interpret it.

#4

Fairfield Homes is developing two parcels near Pigeon Forge, Tennessee. In order to test different advertising approaches, they use different media to reach potential buyers. The mean annual family income for 75 people making inquires at the first development is \$150,000 with a standard deviation of \$40,000. A corresponding sample of 120 people at the second development had a mean of \$180,000 with a standard deviation of \$30,000. At the 0.5 significance level can Fairfield conclude that the population means are different?

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