The grade point averages (GPA) for 12 randomly selected college students are shown on the right. Complete parts (a) through (c) below. Assume the population is normally distributed. a) Find the sample mean. = 2.36 (Round to two decimal places as needed.) b) Find the sample standard deviation. = 1.15 (Round to two decimal places as needed.) c) Construct a 99% confidence interval for the population mean μ: 2.2 3.5 2.7 1.9 0.8 4.0 2.4 1.1 3.7 0.5 2.2 3.3
The grade point averages (GPA) for 12 randomly selected college students are shown on the right. Complete parts (a) through (c) below. Assume the population is normally distributed. a) Find the sample mean. = 2.36 (Round to two decimal places as needed.) b) Find the sample standard deviation. = 1.15 (Round to two decimal places as needed.) c) Construct a 99% confidence interval for the population mean μ: 2.2 3.5 2.7 1.9 0.8 4.0 2.4 1.1 3.7 0.5 2.2 3.3
MATLAB: An Introduction with Applications
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![### Understanding and Computing Confidence Intervals for GPA
Below are the grade point averages (GPA) for 12 randomly selected college students. The data is presented as follows:
```
2.2, 3.5, 2.7, 1.9, 0.8, 4.0, 2.4, 1.1, 3.7, 0.5, 2.2, 3.3
```
The task is to complete the parts (a) through (c) for these GPA values.
Assume the population is normally distributed.
#### (a) Finding the Sample Mean
The sample mean (\( \bar{x} \)) is calculated using the formula:
\[ \bar{x} = \frac{\sum x_i}{n} \]
where \( \sum x_i \) is the sum of all sample values and \( n \) is the number of samples.
Given data:
```
2.2, 3.5, 2.7, 1.9, 0.8, 4.0, 2.4, 1.1, 3.7, 0.5, 2.2, 3.3
```
Sum of values = 28.30\
Number of students (n) = 12
\[ \bar{x} = \frac{28.30}{12} = 2.36 \]
Hence, the sample mean is:
\[ \boxed{2.36} \]
*(Rounded to two decimal places as needed.)*
#### (b) Finding the Sample Standard Deviation
The sample standard deviation (\( s \)) is calculated using the formula:
\[ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} \]
where \( x_i \) represents each individual sample value.
Using the provided values and the previously calculated mean (\( \bar{x} = 2.36 \)), the standard deviation is calculated as:
\[ s = 1.15 \]
So, the sample standard deviation is:
\[ \boxed{1.15} \]
*(Rounded to two decimal places as needed.)*
#### (c) Constructing a 99% Confidence Interval for the Population Mean (\( \mu \))
A 99% confidence interval for the population mean \( \mu \) is computed using the formula](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F952bcd3e-4a7c-474a-8dd6-ddd08471460a%2F3480397b-d4de-44b8-90f0-9a279b8b7d4b%2F36efybl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding and Computing Confidence Intervals for GPA
Below are the grade point averages (GPA) for 12 randomly selected college students. The data is presented as follows:
```
2.2, 3.5, 2.7, 1.9, 0.8, 4.0, 2.4, 1.1, 3.7, 0.5, 2.2, 3.3
```
The task is to complete the parts (a) through (c) for these GPA values.
Assume the population is normally distributed.
#### (a) Finding the Sample Mean
The sample mean (\( \bar{x} \)) is calculated using the formula:
\[ \bar{x} = \frac{\sum x_i}{n} \]
where \( \sum x_i \) is the sum of all sample values and \( n \) is the number of samples.
Given data:
```
2.2, 3.5, 2.7, 1.9, 0.8, 4.0, 2.4, 1.1, 3.7, 0.5, 2.2, 3.3
```
Sum of values = 28.30\
Number of students (n) = 12
\[ \bar{x} = \frac{28.30}{12} = 2.36 \]
Hence, the sample mean is:
\[ \boxed{2.36} \]
*(Rounded to two decimal places as needed.)*
#### (b) Finding the Sample Standard Deviation
The sample standard deviation (\( s \)) is calculated using the formula:
\[ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} \]
where \( x_i \) represents each individual sample value.
Using the provided values and the previously calculated mean (\( \bar{x} = 2.36 \)), the standard deviation is calculated as:
\[ s = 1.15 \]
So, the sample standard deviation is:
\[ \boxed{1.15} \]
*(Rounded to two decimal places as needed.)*
#### (c) Constructing a 99% Confidence Interval for the Population Mean (\( \mu \))
A 99% confidence interval for the population mean \( \mu \) is computed using the formula
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