Chapter 4, Problem 17P

BuyFind*arrow_forward*

10th Edition

Frederick J Gravetter + 1 other

ISBN: 9781305504912

Textbook Problem

For the following sample of n = 8 scores: 0, 1, ½, 0, 3, ½, 0, and 1:

- Simp1ify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6,

0 and 2. Then, compute the mean and standard

deviation for the new sample.

To determine

Mean and standard deviation of a new converted sample and using the result of new sample we need to find the mean standard deviation of old sample

Explanation

Here we have to find the first mean then variance and followed by SD. So, in the calculation part will see how each step has done. And for part b will use part a and the sample values will be half of that and the statistic mean, and SD will follow from this only.

**Given:**

Here y=0, 1, 0.5, 0, 3, 0.5,0,1 and n=8, samples are given

**Formula Used:**

For sample of size n, we have below formulas

Mean=

Variance=

Standard Deviation (SD)=

[we know the properties of mean and Variance

Define,

Y=X+b

Z=a*X

To find the mean and Variance of Y and Z

Where X having mean m and Variance s^{2}

E(Y) =E (X +b) =E(X) +b=m+b; var(Y) =Var(X) = s^{2}

E(z)=a*E(X)=a*m; Var(Z)=var(X)*a^{2}= s^{2}*a^{2}

Here a and b are arbitrary constant]

**Calculation:**

a)

Y | X=2*y | (x- |

0 | 0 | 2.25 |

1 | 2 | 0.25 |

0.5 | 1 | 0.25 |

0 | 0 | 2.25 |

3 | 6 | 20.25 |

0.5 | 1 | 0.25 |

0 | 0 | 2 |

Essentials Of Statistics

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Calculus (MindTap Course List)

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus (MindTap Course List)

Calculus: An Applied Approach (MindTap Course List)

Calculus: Early Transcendental Functions

Calculus: Early Transcendentals

Multivariable Calculus

Applied Calculus

Single Variable Calculus: Early Transcendentals, Volume I

Finite Mathematics and Applied Calculus (MindTap Course List)

Probability and Statistics for Engineering and the Sciences

Understanding Basic Statistics

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Single Variable Calculus

Finite Mathematics

Mathematical Excursions (MindTap Course List)

Elementary Geometry For College Students, 7e

Elementary Technical Mathematics

Intermediate Algebra

Mathematical Applications for the Management, Life, and Social Sciences

Calculus of a Single Variable

Single Variable Calculus: Early Transcendentals

Contemporary Mathematics for Business & Consumers

Trigonometry (MindTap Course List)

Elements Of Modern Algebra

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Study Guide for Stewart's Multivariable Calculus, 8th

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Geometry for College Students

Calculus: Early Transcendental Functions (MindTap Course List)