I am trying to understand how to use this formula from an example question. In the example question, p(Obs) is .167, p(Pop) is .2, and N is 24. The answer is z = -.4024 but I don't know why that is the answer. Can you help?
I am trying to understand how to use this formula from an example question. In the example question, p(Obs) is .167, p(Pop) is .2, and N is 24. The answer is z = -.4024 but I don't know why that is the answer. Can you help?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I am trying to understand how to use this formula from an example question. In the example question, p(Obs) is .167, p(Pop) is .2, and N is 24. The answer is z = -.4024 but I don't know why that is the answer. Can you help?
![**Formula for Calculating Z-Score**
The Z-score formula is used to determine how many standard deviations a particular observation (Obs) is from the population mean (Pop). The formula is expressed as follows:
\[
Z = \frac{P(Obs) - P(Pop)}{\sqrt{\frac{P(Pop) \times \left(1 - P(Pop)\right)}{N}}}
\]
**Explanation:**
- **P(Obs):** The proportion observed in the sample.
- **P(Pop):** The proportion in the population.
- **N:** The sample size.
**Usage:**
This formula helps in assessing the rarity or commonness of the observed proportion with respect to the known population proportion. It is commonly used in statistics for hypothesis testing and normal distribution analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F148a357d-8cdd-416f-be99-43df2fa0f718%2Fb836b6b8-0f70-425c-a9c7-1593f4eeafef%2Fyor71xq_processed.png&w=3840&q=75)
Transcribed Image Text:**Formula for Calculating Z-Score**
The Z-score formula is used to determine how many standard deviations a particular observation (Obs) is from the population mean (Pop). The formula is expressed as follows:
\[
Z = \frac{P(Obs) - P(Pop)}{\sqrt{\frac{P(Pop) \times \left(1 - P(Pop)\right)}{N}}}
\]
**Explanation:**
- **P(Obs):** The proportion observed in the sample.
- **P(Pop):** The proportion in the population.
- **N:** The sample size.
**Usage:**
This formula helps in assessing the rarity or commonness of the observed proportion with respect to the known population proportion. It is commonly used in statistics for hypothesis testing and normal distribution analysis.
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