Chapter 9: Q .11. (page 564)

How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is $179.6$ ml and the standard deviation is $1.3$ ml. A significance test yields a $P$ -value of $0.0589$ . Interpret the $P$ -value.

Short Answer

Expert verified

There is a $5.89 %$ possibility that the mean volume of liquid in a sample of $40$ bottles is $179.6$ millilitres or more extreme, when the mean volume of liquid of all bottles is $180$ millilitres

Step by step solution

Step 1:Given information

The mean amount of liquid in the bottles is $179.6$ $ml$ and the standard deviation is $1.3 ml$ . A significance test yields a $P$ -value of $0.0589$

Step 2:Explaination

$P = 0.0589 = 5.89 %$

$\bar{x} = 179.6$

$s = 1.3$

Claim is mean is $180$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population mean is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

$H_{0} : μ = 180$

$H_{a} : μ \neq 180$

The P-value is the probability of getting the value of the test static or a value more extreme, when the null hypothesis is true.

There is a

5.89 %

possibility that the mean volume of liquid in a sample of 40 bottles is

179.6

millilitres or more extreme, when the mean volume of liquid of all bottles is

180

millilitres

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.

How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is $179.6$ ml and the standard deviation is $1.3$ ml. A significance test yields a $P$ -value of $0.0589$ . Interpret the $P$ -value.

Short Answer

Step by step solution

Step 1:Given information

Step 2:Explaination

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is 179.6ml and the standard deviation is 1.3ml. A significance test yields a P-value of 0.0589. Interpret the P-value.

Short Answer

Step by step solution

Step 1:Given information

Step 2:Explaination

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is $179.6$ ml and the standard deviation is $1.3$ ml. A significance test yields a $P$ -value of $0.0589$ . Interpret the $P$ -value.