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Statistic problems - The null and alternate hypothesis

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#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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Solution Summary

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.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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