You take a random sample of 20 female toco toucans, and you find that they have an average body mass of 546.47 grams with a standard deviation of 104.87 grams. You may assume the sampling distribution is nearly normal. Calculate a 95% confidence interval for the mean body mass of a female toco toucan. Please write your answers to at least four places. a. Critical value: t* = b. Standard error: 23.44964 c. Margin of error: d. Confidence interval: <μ<
You take a random sample of 20 female toco toucans, and you find that they have an average body mass of 546.47 grams with a standard deviation of 104.87 grams. You may assume the sampling distribution is nearly normal. Calculate a 95% confidence interval for the mean body mass of a female toco toucan. Please write your answers to at least four places. a. Critical value: t* = b. Standard error: 23.44964 c. Margin of error: d. Confidence interval: <μ<
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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how do i solve parts a, c, and d?
![This image contains a statistical exercise aimed at calculating a 95% confidence interval for the mean body mass of female toco toucans, based on a sample.
Here is the transcription suitable for an educational website:
---
## Confidence Interval Calculation for Toco Toucans
You take a random sample of 20 female toco toucans, and you find that they have an average body mass of 546.47 grams with a standard deviation of 104.87 grams. You may assume the sampling distribution is nearly normal.
**Objective:** Calculate a 95% confidence interval for the mean body mass of a female toco toucan. Please write your answers to at least four places.
### Step-by-Step Instructions
a. **Critical value:** \( t^* = \) [ ______ ]
b. **Standard error:**
\[ \text{Standard error} = \frac{\text{Standard deviation}}{\sqrt{\text{Sample size}}} \]
\[ \text{Standard error} = 23.44964 \]
c. **Margin of error:** [ ______ ]
d. **Confidence interval:**
\[ < \mu < \]
\[ [ \text{Enter lower bound} ] < \mu < [ \text{Enter upper bound} ] \]
### Explanation of Terms
- **Critical value \( t \)**: The value from the t-distribution that corresponds to the desired confidence level.
- **Standard error**: A measure of how much the sample mean is expected to vary from the true population mean.
- **Margin of error**: The range above and below the sample mean within which the true population mean is expected to lie.
- **Confidence interval**: A range of values that is likely to contain the population mean with a certain level of confidence.
---
**Note:** There are no graphs or diagrams in the image. The exercise involves only text and numerical inputs.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8e28faf-547f-4c48-bb6d-e40546588d1c%2F56ad7b19-4287-4180-bac3-11ad3363ce65%2Fi6wtje_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This image contains a statistical exercise aimed at calculating a 95% confidence interval for the mean body mass of female toco toucans, based on a sample.
Here is the transcription suitable for an educational website:
---
## Confidence Interval Calculation for Toco Toucans
You take a random sample of 20 female toco toucans, and you find that they have an average body mass of 546.47 grams with a standard deviation of 104.87 grams. You may assume the sampling distribution is nearly normal.
**Objective:** Calculate a 95% confidence interval for the mean body mass of a female toco toucan. Please write your answers to at least four places.
### Step-by-Step Instructions
a. **Critical value:** \( t^* = \) [ ______ ]
b. **Standard error:**
\[ \text{Standard error} = \frac{\text{Standard deviation}}{\sqrt{\text{Sample size}}} \]
\[ \text{Standard error} = 23.44964 \]
c. **Margin of error:** [ ______ ]
d. **Confidence interval:**
\[ < \mu < \]
\[ [ \text{Enter lower bound} ] < \mu < [ \text{Enter upper bound} ] \]
### Explanation of Terms
- **Critical value \( t \)**: The value from the t-distribution that corresponds to the desired confidence level.
- **Standard error**: A measure of how much the sample mean is expected to vary from the true population mean.
- **Margin of error**: The range above and below the sample mean within which the true population mean is expected to lie.
- **Confidence interval**: A range of values that is likely to contain the population mean with a certain level of confidence.
---
**Note:** There are no graphs or diagrams in the image. The exercise involves only text and numerical inputs.
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