First, let's assume that before collecting data, we, as researchers, have decided that a probability smaller than 5% is “a small probability". Recall that an event with a small probability means "the event is unlikely to happen". (Other probability numbers that are typically considered "small" include 1%, 3%, etc.) Assume that the population mean is 23.4 cm (that's our assumption). If we imagine that we repeat taking all possible samples of size 25 from the population, then only about out of sample means will have values as small as cm or even smaller. In other words, if the population mean is indeed 23.4 cm, the chances that such extremely small sample means would occur by pure chance alone are small (since the probability calculated from #15 is smaller than our threshold of 5%). To put it another way, if the population mean is indeed 23.4 cm, then we would NOT expect a sample mean as small as to occur if we only select one single sample. (But if such an extreme sample mean does occur, it implies that there is something else, other than pure chance, is at play. That "something else" is that the assumption could be wrong after all because if the assumption is true, such an extreme sample mean should not happen.) a. 1, 10, 23.4, 23.4 b. 1, 100, 22.62, 22.62 c. 1, 100, 23.4, 22.62 d. 1, 1000, 23.4, 23.4
First, let's assume that before collecting data, we, as researchers, have decided that a probability smaller than 5% is “a small probability". Recall that an event with a small probability means "the event is unlikely to happen". (Other probability numbers that are typically considered "small" include 1%, 3%, etc.) Assume that the population mean is 23.4 cm (that's our assumption). If we imagine that we repeat taking all possible samples of size 25 from the population, then only about out of sample means will have values as small as cm or even smaller. In other words, if the population mean is indeed 23.4 cm, the chances that such extremely small sample means would occur by pure chance alone are small (since the probability calculated from #15 is smaller than our threshold of 5%). To put it another way, if the population mean is indeed 23.4 cm, then we would NOT expect a sample mean as small as to occur if we only select one single sample. (But if such an extreme sample mean does occur, it implies that there is something else, other than pure chance, is at play. That "something else" is that the assumption could be wrong after all because if the assumption is true, such an extreme sample mean should not happen.) a. 1, 10, 23.4, 23.4 b. 1, 100, 22.62, 22.62 c. 1, 100, 23.4, 22.62 d. 1, 1000, 23.4, 23.4
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Sure! Here's the transcription of the image for an educational website:
---
**1. Left-tail probability**
Refer to #15 in Ch 13 multiple choice. The interpretation of \( P(\bar{x} < 22.62) \) is as follows:
First, let’s assume that before collecting data, we, as researchers, have decided that a probability smaller than 5% is “a small probability”. Recall that an event with a small probability means “the event is unlikely to happen”. (Other probability numbers that are typically considered “small” include 1%, 3%, etc.)
Assume that the population mean is 23.4 cm (that’s our assumption). If we imagine that we repeat taking all possible samples of size 25 from the population, then only about [blank] out of [blank] sample means will have values as small as [blank] cm or even smaller. In other words, if the population mean is indeed 23.4 cm, the chances that such extremely small sample means would occur by pure chance alone are small (since the probability calculated from #15 is smaller than our threshold of 5%).
To put it another way, if the population mean is indeed 23.4 cm, then we would NOT expect a sample mean as small as [blank] to occur if we only select one single sample. (But if such an extreme sample mean does occur, it implies that there is something else, other than pure chance, at play. That “something else” is that the assumption could be wrong after all because if the assumption is true, such an extreme sample mean should not happen.)
a. 1, 10, 23.4, 23.4
b. 1, 100, 22.62, 22.62
c. 1, 100, 23.4, 22.62
d. 1, 1000, 23.4, 23.4
---
There are no graphs or diagrams that require explanation in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F223000e0-2da9-427a-b6d1-be5081a09103%2Fe104fe03-23b9-4dd8-8b18-ff5072df0f8d%2Fnxlln46_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Sure! Here's the transcription of the image for an educational website:
---
**1. Left-tail probability**
Refer to #15 in Ch 13 multiple choice. The interpretation of \( P(\bar{x} < 22.62) \) is as follows:
First, let’s assume that before collecting data, we, as researchers, have decided that a probability smaller than 5% is “a small probability”. Recall that an event with a small probability means “the event is unlikely to happen”. (Other probability numbers that are typically considered “small” include 1%, 3%, etc.)
Assume that the population mean is 23.4 cm (that’s our assumption). If we imagine that we repeat taking all possible samples of size 25 from the population, then only about [blank] out of [blank] sample means will have values as small as [blank] cm or even smaller. In other words, if the population mean is indeed 23.4 cm, the chances that such extremely small sample means would occur by pure chance alone are small (since the probability calculated from #15 is smaller than our threshold of 5%).
To put it another way, if the population mean is indeed 23.4 cm, then we would NOT expect a sample mean as small as [blank] to occur if we only select one single sample. (But if such an extreme sample mean does occur, it implies that there is something else, other than pure chance, at play. That “something else” is that the assumption could be wrong after all because if the assumption is true, such an extreme sample mean should not happen.)
a. 1, 10, 23.4, 23.4
b. 1, 100, 22.62, 22.62
c. 1, 100, 23.4, 22.62
d. 1, 1000, 23.4, 23.4
---
There are no graphs or diagrams that require explanation in the image.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman