   Chapter 7, Problem 17P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

For random samples of size n = 25 selected from a normal distribution with a mean of μ = 50 and a standard deviation of σ = 20, find each of the following: a. The range of sample means that defines the middle 95% of the distribution of sample means. b. The range of sample means that defines the middle 99% of the distribution of sample means.

a.

To determine
The range of sample means that defines the middle 95% of the distribution of sample means.

Explanation

Given info:

Sample size is given as n=25.

Population mean is μ=50.

Population standard deviation is σ=20.

Confidence interval is given as 95%.

Calculation:

The symbols μ and σ represent the population mean and standard deviation respectively. Let M represents sample mean. Then for calculating the range need to find standard error:

σM=σn=2025=205=4

Now the z score value for middle 95% or for two tailed with alpha level 0.05 using z table is ±1.96. Now for calculating range of sample means:

μ=M±z(se)

Where, z is for z score and se for standard error

b.

To determine
The range of sample means that defines the middle 99% of the distribution of sample means.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 