This wine stinks. How sensitive are the untrained noses of students? Exercise 16.27 (page 390) gives the lowest levels of dimethyl sulfide (DMS) that 10 students could detect. You want to estimate the mean DMS odor threshold among all students and you would be satis-

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question

needs to be solved with calculator please ti 83 or 84

**Transcription for Educational Resource**

**Understanding DMS Sensitivity in Students**

*Exercise 16.27 discusses an intriguing aspect of sensory science: the detection sensitivity of untrained student noses to dimethyl sulfide (DMS). This exercise found on page 390, explores the minimal concentrations of DMS that 10 student participants were able to detect.*

**Research Objective:**
The goal is to determine the average DMS odor detection threshold among all students. The aim is to achieve a precise estimation of the mean, with the allowance of an error margin of ±0.1 at a 99% confidence level.

**Statistical Parameters:**
The standard deviation for the detection threshold, based on existing data for untrained noses, is given as σ = 7 micrograms per liter of wine.

**Research Question:**
To satisfy these statistical accuracy requirements, what should be the size of the Simple Random Sample (SRS) of untrained students?

**Discussion:**
This scenario presents a classic problem in statistical estimation, dealing with sample size determination. Calculating the required SRS size involves understanding the relationships between sample size, confidence intervals, and standard deviations.
Transcribed Image Text:**Transcription for Educational Resource** **Understanding DMS Sensitivity in Students** *Exercise 16.27 discusses an intriguing aspect of sensory science: the detection sensitivity of untrained student noses to dimethyl sulfide (DMS). This exercise found on page 390, explores the minimal concentrations of DMS that 10 student participants were able to detect.* **Research Objective:** The goal is to determine the average DMS odor detection threshold among all students. The aim is to achieve a precise estimation of the mean, with the allowance of an error margin of ±0.1 at a 99% confidence level. **Statistical Parameters:** The standard deviation for the detection threshold, based on existing data for untrained noses, is given as σ = 7 micrograms per liter of wine. **Research Question:** To satisfy these statistical accuracy requirements, what should be the size of the Simple Random Sample (SRS) of untrained students? **Discussion:** This scenario presents a classic problem in statistical estimation, dealing with sample size determination. Calculating the required SRS size involves understanding the relationships between sample size, confidence intervals, and standard deviations.
The image displays a table titled "SOME COMMON VALUES OF Z*". This table outlines critical values (Z*) associated with various confidence levels and their corresponding tail probabilities. The information is organized into three columns:

1. **Confidence Level**: This column lists the percentage of the confidence level commonly used in statistical analysis, ranging from 60% to 99%.

2. **Tail Level**: This column indicates the proportion of the probability in the tails of the standard normal distribution. This essentially represents the probability that lies outside the central confidence level. The values range from 0.20 to 0.005.

3. **Z***: This column provides the critical Z* values for each confidence level, which are used to calculate confidence intervals in a normal distribution. The Z* values range from 0.84 to 2.576.

Here is the detailed transcription of the table:

- **60% Confidence Level**
  - Tail Level: 0.20
  - Z*: 0.84
 
- **80% Confidence Level**
  - Tail Level: 0.10
  - Z*: 1.28

- **90% Confidence Level**
  - Tail Level: 0.05
  - Z*: 1.645

- **95% Confidence Level**
  - Tail Level: 0.025
  - Z*: 1.96

- **96% Confidence Level**
  - Tail Level: 0.02
  - Z*: 2.05

- **98% Confidence Level**
  - Tail Level: 0.01
  - Z*: 2.33

- **99% Confidence Level**
  - Tail Level: 0.005
  - Z*: 2.576

These values are pivotal for statistical tasks such as hypothesis testing and constructing confidence intervals, allowing for meaningful interpretation of data results.
Transcribed Image Text:The image displays a table titled "SOME COMMON VALUES OF Z*". This table outlines critical values (Z*) associated with various confidence levels and their corresponding tail probabilities. The information is organized into three columns: 1. **Confidence Level**: This column lists the percentage of the confidence level commonly used in statistical analysis, ranging from 60% to 99%. 2. **Tail Level**: This column indicates the proportion of the probability in the tails of the standard normal distribution. This essentially represents the probability that lies outside the central confidence level. The values range from 0.20 to 0.005. 3. **Z***: This column provides the critical Z* values for each confidence level, which are used to calculate confidence intervals in a normal distribution. The Z* values range from 0.84 to 2.576. Here is the detailed transcription of the table: - **60% Confidence Level** - Tail Level: 0.20 - Z*: 0.84 - **80% Confidence Level** - Tail Level: 0.10 - Z*: 1.28 - **90% Confidence Level** - Tail Level: 0.05 - Z*: 1.645 - **95% Confidence Level** - Tail Level: 0.025 - Z*: 1.96 - **96% Confidence Level** - Tail Level: 0.02 - Z*: 2.05 - **98% Confidence Level** - Tail Level: 0.01 - Z*: 2.33 - **99% Confidence Level** - Tail Level: 0.005 - Z*: 2.576 These values are pivotal for statistical tasks such as hypothesis testing and constructing confidence intervals, allowing for meaningful interpretation of data results.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Fractions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON