Find the value of tn-1,? needed to construct an upper or

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

ISBN: 9780073401331 38

Solution for problem 2E Chapter 5.3

Statistics for Engineers and Scientists | 4th Edition

Textbook Solutions
2901 Step-by-step solutions solved by professors and subject experts
Get 24/7 help from StudySoup virtual teaching assistants

Statistics for Engineers and Scientists | 4th Edition

4 5 1 267 Reviews

Problem 2E

Find the value of tn-1,α needed to construct an upper or lower confidence bound in each of the situations in Exercise 1.

Step-by-Step Solution:

Answer:

Step 1 of 5:

Here we have to find the value of ${t}_{n-1,\ \alpha{}}$ needed to construct an upper or lower confidence bound in each of the given level with the given sample size in exercise 1.

Step 2 of 5:

a). Given that the confidence level is 90% and the sample size is n = 12.

Then,

$(1-\alpha{})$ % = 90% = $\frac{90}{100}=0.9$

(1 - 0.9) = 0.1

Therefore,

The level of significance $\alpha{}=0.1$

And the degrees of freedom, DF = n - 1

= 12-1

= 11

Therefore, the critical value of ‘t’ is

${t}_{12-1,0.1}=1.363$ ( This value from statistical table, 11th row and 0.1 column)

Then,

Lower bound < t < upper bound

-1.363 < t < 1.363

$-1.363<\frac{\overline{x}-\mu{}}{\frac{s}{\sqrt{n}}}<1.363$

Step 3 of 5:

b). Given that the confidence level is 95% and the sample size is n = 7.

Then,

$(1-\alpha{})$ % = 95% = $\frac{95}{100}=0.95$

(1 - 0.95) = 0.05

Therefore,

The level of significance $\alpha{}=0.05$

And the degrees of freedom, DF = n - 1

= 7-1

= 6

Therefore, the critical value of ‘t’ is

${t}_{7-1,0.05}=1.943$ ( This value from statistical table, 6th row and 0.05 column)

Then,

Lower bound < t < upper bound

-1.943 < t < 1.943

$-1.943<\frac{\overline{x}-\mu{}}{\frac{s}{\sqrt{n}}}<1.943$

Step 4 of 5

Chapter 5.3, Problem 2E is Solved

Step 5 of 5

Textbook: Statistics for Engineers and Scientists

Edition: 4

Author: William Navidi

ISBN: 9780073401331

This full solution covers the following key subjects: Bound, confidence, construct, exercise, Find. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 2E from chapter: 5.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 2E from 5.3 chapter was answered, more than 248 students have viewed the full step-by-step answer. The answer to “Find the value of tn-1,? needed to construct an upper or lower confidence bound in each of the situations in Exercise 1.” is broken down into a number of easy to follow steps, and 22 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.