Did I calculate (a) through (e) correctly? I am having trouble with f and g. For g: I am 95% confident that in eight subjects who have a category fluency test score will score somewhere between 6 and 11??For G: In repeated sampling, this method produces intervals that capture the sample mean in about 95% of samples??Thank you ### Understanding Early Alzheimer’s Disease: A Statistical Analysis#### Study OverviewIn a study examining the effect of early Alzheimer’s disease on nondeclarative memory, researchers used the Category Fluency Test to establish baseline persistence and semantic memory and language abilities. The eight subjects in the sample had Category Fluency Test scores of 11, 10, 6, 3, 11, 10, 9, 11.#### Analysis BreakdownThe following steps detail the statistical analysis performed on the sample data:1. **Point Estimate of the Population Mean (a)**: - Raw scores: $11, 10, 6, 3, 11, 10, 9, 11$ - \[ \bar{X} = \frac{\sum{X}}{n} = \frac{71}{8} = 8.875 \] - The point estimate of the population mean is 8.875.2. **Standard Deviation of the Sample (b)**: - Calculation: \[ s^2 = \frac{\sum{(X - \bar{X})^2}}{n-1} = \frac{689 - \left(\frac{71^2}{8}\right)}{8-1} = 8.410714286 \] \[ s = \sqrt{8.410714286} = 2.90012315 \] - The standard deviation $ s $ is 2.90012315.3. **Estimated Standard Error of the Sample Mean (c)**: - Calculation: \[ \sigma_{\bar{X}} = \frac{s}{\sqrt{n}} = \frac{2.90012315}{\sqrt{8}} = 0.3625153938 \] - The estimated standard error is 0.3625153938.4. **95% Confidence Interval for the Population Mean (d)**: - For $ n = 8 $ and $ df = 7 $, the critical value $ t_{c} $ from t-distribution table at 95% confidence is 2.365. - Calculation: \[ \bar{X} \pm t_{c} \left( \frac{s}{\sqrt{n}} \right) =

Name: Did I calculate (a) through (e) correctly? I am having trouble with f
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Did I calculate (a) through (e) correctly? I am having trouble with f and g. For g: I am 95% confident that in eight subjects who have a category fluency test score will score somewhere between 6 and 11??For G: In repeated sampling, this method prod

It is mentioned that the population follows normal distribution and population standard deviation is…

Answered: 6.3.2 In a study of the effects of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

100%

Did I calculate (a) through (e) correctly? I am having trouble with f and g. For g: I am 95% confident that in eight subjects who have a category fluency test score will score somewhere between 6 and 11??

For G: In repeated sampling, this method produces intervals that capture the sample mean in about 95% of samples??

Thank you

### Understanding Early Alzheimer’s Disease: A Statistical Analysis

#### Study Overview
In a study examining the effect of early Alzheimer’s disease on nondeclarative memory, researchers used the Category Fluency Test to establish baseline persistence and semantic memory and language abilities. The eight subjects in the sample had Category Fluency Test scores of 11, 10, 6, 3, 11, 10, 9, 11.

#### Analysis Breakdown
The following steps detail the statistical analysis performed on the sample data:

1. **Point Estimate of the Population Mean (a)**:
- Raw scores: $11, 10, 6, 3, 11, 10, 9, 11$
- \[
\bar{X} = \frac{\sum{X}}{n} = \frac{71}{8} = 8.875
\]
- The point estimate of the population mean is 8.875.

2. **Standard Deviation of the Sample (b)**:
- Calculation:
\[
s^2 = \frac{\sum{(X - \bar{X})^2}}{n-1} = \frac{689 - \left(\frac{71^2}{8}\right)}{8-1} = 8.410714286
\]
\[
s = \sqrt{8.410714286} = 2.90012315
\]
- The standard deviation $ s $ is 2.90012315.

3. **Estimated Standard Error of the Sample Mean (c)**:
- Calculation:
\[
\sigma_{\bar{X}} = \frac{s}{\sqrt{n}} = \frac{2.90012315}{\sqrt{8}} = 0.3625153938
\]
- The estimated standard error is 0.3625153938.

4. **95% Confidence Interval for the Population Mean (d)**:
- For $ n = 8 $ and $ df = 7 $, the critical value $ t_{c} $ from t-distribution table at 95% confidence is 2.365.
- Calculation:
\[
\bar{X} \pm t_{c} \left( \frac{s}{\sqrt{n}} \right) =

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Propositional Calculus$

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.

Similar questions