Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q. 7.29 (page 300)

Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.

Short Answer

Expert verified

Yes, the sample size has an effect on the standard deviation of all possible sample means.

Step by step solution

01

Step 1. Given Information

We need to identify whether the sample size has an effect on the standard deviation of all possible sample means.

02

Step 2. Explanation

For samples of size n,the standard deviation of the variable x¯equals the standard deviation of the variable under consideration divided by the square root of the sample size. That is, σx¯=σn.

So, it can be seen that the standard deviation of all possible sample means depends on the sample size n.

And it can be seen that as the sample size increase the standard deviation ofx¯decreases.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Consider simple random samples of size n without replacement from a population of size N.

Part (a): Show that if n≤0.05N,then0.97≤N-nN-1≤1,

Part (b): Use part (a) to explain why there is little difference in the values provided by Equations (7.1)and (7.2)when the sample size is small relative to the population size- that is, when the size of the sample does not exceed 5% of the size of the population.

Part (c): Explain why the finite population correction factor can be ignored and the simpler formula, Equation (7.2), can be used when the sample size is small relative to the population size.

Part (d): The term N-n/N-1is known as the finite population correction factor. Can you explain why?

7.16 NBA Champs. This exercise requires that you have done Exercises 7.11-7.15.
a. Draw a graph similar to that shown in Fig. 7.3 on page 294for sample sizes of 1,2,3,4, and 5.
b. What does your graph in part (a) illustrate about the impact of increasing sample size on sampling error?
c. Construct a table similar to Table 7.4 on page 294 for some values of your choice.

NBA Champs Repeat parts (b) and (c) of Exercise 7.41 for samples of size 4. For part (b), use your answer to Exercise 7.14(b).

Menopause in Mexico. In the article "Age at Menopause in Puebla. Mexico" (Human Biology, Vol. 75, No, 2, Pp. 205-206), authors L. Sievert and S. Hautaniemi compared the age of menopause for different populations. Menopause, the last menstrual period, is a universal phenomenon among females. According to the article, the mean age of menopause, surgical or natural, in Puebla, Mexico is 44.8 years with a standard deviation of 5.87 years. Letx¯ denote the mean age of menopause for a sample of females in Puebla, Mexico.
a. For samples of size 40, find the mean and standard deviation of x¯. Interpret your results in words.
b. Repeat part (a) with n=120.

Ethanol Railroad Tariffs. An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is \(1,150, determine the probability that the mean tariff rate of 500randomly selected railroad car shipments of ethanol will be within \)100of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free