Chapter 8: Q. 9.78 (page 380)

We have been provided a sample mean, sample size, and population standard deviation. In the given case, use the one-mean z-test to perform the required hypothesis test at the $5 %$ significance level.
$\bar{x} = 21, n = 32, σ = 4, H_{0} : μ = 22, H_{a} : μ < 22$

Short Answer

Expert verified

The value of z is $- 1.41$ , critical value is $- 1.645$ , $P = 0.002$ and reject $H_{0}$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\bar{x} = 21, n = 32, σ = 4, H_{0} : μ = 22, H_{a} : μ < 22$

Step 2. Consider the test hypothesis.

Consider the given hypothesis,

$μ$ is the population mean.

The test hypothesis,

$H_{0} : μ = 22 V s H_{a} : μ < 22$

Therefore, the test is left tailed test.

And the level of significance is $α = 0.05$ .

Step 3. Use the test statistics.

We want to find the hypothesis test about the mean $μ$ ,

$z = \frac{\bar{x} - μ_{0}}{\frac{σ}{\sqrt{n}}} = \frac{21 - 22}{\frac{4}{\sqrt{32}}} = - 1.41$

Therefore, this is left tailed test with $α = 0.05$ , the critical value is $- z_{a} = - z_{0.05} = - 1.645$

The rejection region is $z < - z_{0.05}$ .

Here, data-custom-editor="chemistry" $z = - 1.41 > - 1.645$ .

Therefore, we do not reject $H_{0}$ at $5 %$ level of significance as the value of the test statistics z does not fall in the rejection region.

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!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

We have been provided a sample mean, sample size, and population standard deviation. In the given case, use the one-mean z-test to perform the required hypothesis test at the $5 %$ significance level.
$\bar{x} = 21, n = 32, σ = 4, H_{0} : μ = 22, H_{a} : μ < 22$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Consider the test hypothesis.

Step 3. Use the test statistics.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

We have been provided a sample mean, sample size, and population standard deviation. In the given case, use the one-mean z-test to perform the required hypothesis test at the 5%significance level.x¯=21,n=32,σ=4,H0:μ=22,Ha:μ<22

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Consider the test hypothesis.

Step 3. Use the test statistics.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

We have been provided a sample mean, sample size, and population standard deviation. In the given case, use the one-mean z-test to perform the required hypothesis test at the $5 %$ significance level.
$\bar{x} = 21, n = 32, σ = 4, H_{0} : μ = 22, H_{a} : μ < 22$