What is the SRS size ? To estimate the mean score $ \mu $ of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS (Simple Random Sample) of students. From published information, you know that the scores are approximately Normal with a standard deviation of about 6.6. You want your sample mean $ \bar{x} $ to estimate $ \mu $ with an error of no more than 0.9 point in either direction.(a) What standard deviation must $ \bar{x} $ have so that 99.7% of all samples give an $ \bar{x} $ within 0.9 point of $ \mu $? Use the 68-95-99.7 rule (also known as the Empirical Rule). (Enter your answer rounded to four decimal places.)\[\text{standard deviation of } \bar{x} = 0.3\] **Transcription of Image Text:**---**(b) How large an SRS do you need in order to reduce the standard deviation of $\bar{x}$ to the value you found? (Enter your answer rounded to the nearest whole number.)**SRS size = [_____________]---*Note:* SRS stands for Simple Random Sample, a method often used in statistical analysis to ensure each member of a population has an equal chance of being chosen.**Additional Details:**- **Contextual Information:** This question appears to be from an educational resource about statistics.- **Source:** This question is sourced from "Moore, The Basic Practice Of Statistics, 8e," published by W.H. Freeman.- **Interface Details:** The question is displayed on a laptop screen with a visible toolbar featuring various applications like a web browser, Amazon, Dropbox, and Skype, suggesting it's part of a digital educational tool or platform. The time and date indication shows it's early morning on November 8, 2020.

From the provided information, Population standard deviation (σ) = 6.6 Margin of error (E) = 0.9 Confidence level = 99.7%The z value at 99.7% confidence level from the standard normal table is 2.9677. The required sample size can be obtained as:

Answered: (b) How large an SRS do you need in…

Math

Statistics

(b) How large an SRS do you need in order to reduce the standard deviation of x to the value you found? (Enter your answer rounded to the nearest whole number.) SRS size =

MATLAB: An Introduction with Applications

6th Edition

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Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

What is the SRS size ?

To estimate the mean score $ \mu $ of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS (Simple Random Sample) of students. From published information, you know that the scores are approximately Normal with a standard deviation of about 6.6. You want your sample mean $ \bar{x} $ to estimate $ \mu $ with an error of no more than 0.9 point in either direction.

(a) What standard deviation must $ \bar{x} $ have so that 99.7% of all samples give an $ \bar{x} $ within 0.9 point of $ \mu $? Use the 68-95-99.7 rule (also known as the Empirical Rule). (Enter your answer rounded to four decimal places.)

\[
\text{standard deviation of } \bar{x} = 0.3
\]

**Transcription of Image Text:**

---

**(b) How large an SRS do you need in order to reduce the standard deviation of $\bar{x}$ to the value you found? (Enter your answer rounded to the nearest whole number.)**

SRS size = [_____________]

---

*Note:* SRS stands for Simple Random Sample, a method often used in statistical analysis to ensure each member of a population has an equal chance of being chosen.

**Additional Details:**

- **Contextual Information:** This question appears to be from an educational resource about statistics.
- **Source:** This question is sourced from "Moore, The Basic Practice Of Statistics, 8e," published by W.H. Freeman.
- **Interface Details:** The question is displayed on a laptop screen with a visible toolbar featuring various applications like a web browser, Amazon, Dropbox, and Skype, suggesting it's part of a digital educational tool or platform. The time and date indication shows it's early morning on November 8, 2020.

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