Did I calculate this correctly? Thank you. ### Constructing a 95% Confidence Interval for Mean Monthly Salary- **Problem Statement:** The mean monthly salary of a random sample of 25 college graduates under the age of 35 was found to be $2425 with a standard deviation of $635. Assume that the distribution of monthly salaries for all college graduates under the age of 35 is approximately normally distributed. We need to construct a 95% confidence interval for the population mean of monthly salaries of all college graduates under the age of 35.#### Given Data:- Sample size ($ n $): 25- Sample mean ($ \overline{X} $): $2425- Standard deviation ($ s $): $635#### Step-by-Step Solution:1. **Determine the degrees of freedom (d.f.):** \[ \text{d.f.} = n - 1 = 25 - 1 = 24 \]2. **Find the critical value ($ t_c $) for a 95% confidence interval** - From the $ t $-distribution table, for 24 degrees of freedom and a 95% confidence level, ($ \alpha/2 = 0.025 $), the critical value ($ t_c $) is approximately 2.064.3. **Applying the formula for the confidence interval:** \[ \overline{X} \pm t_c \left( \frac{s}{\sqrt{n}} \right) \]4. **Plugging in the values:** \[ 2425 \pm 2.064 \left( \frac{635}{\sqrt{25}} \right) \] \[ 2425 \pm 2.064 \left( \frac{635}{5} \right) \] \[ 2425 \pm 2.064 \times 127 \] \[ 2425 \pm 262.128 \]5. **Calculate the intervals:** \[ \text{Lower bound} = 2425 - 262.128 = 2162.872 \] \[ \text{Upper bound} = 2425 + 262.128 = 2687.128 \]#### Conclusion:The 95% confidence interval for

Name: Did I calculate this correctly? Thank you. ### Constructing a 95% Conf
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Did I calculate this correctly? Thank you. ### Constructing a 95% Confidence Interval for Mean Monthly Salary- **Problem Statement:** The mean monthly salary of a random sample of 25 college graduates under the age of 35 was found to be $2425 with a

We have given that Sample size n=25 , sample mean xbar=2425 , and standard deviation s=635 tc=2.064…

Math

Statistics

7. The mean monthly salary of a random sample of 25 college graduates under the age of 35 was found to be $2425 with a standard deviation of $635 Assume that the distribution of monthly salaries for all college graduates under the age of 35 is approximately normally distributed. Construct a 95% confidence interval for u, the population mean of monthly salaries of all college graduates under the 35. age of n= as &=2425 S= 635 d.f= n-1 = 25-1 d.f.= 24 9520 C.I = 1.96 ヌキt。% 2=.25 950 /2:.25 2425+20/635 Vas t=2064 287, 2687.13

7. The mean monthly salary of a random sample of 25 college graduates under the age of 35 was found to be $2425 with a standard deviation of $635 Assume that the distribution of monthly salaries for all college graduates under the age of 35 is approximately normally distributed. Construct a 95% confidence interval for u, the population mean of monthly salaries of all college graduates under the 35. age of n= as &=2425 S= 635 d.f= n-1 = 25-1 d.f.= 24 9520 C.I = 1.96 ヌキt。% 2=.25 950 /2:.25 2425+20/635 Vas t=2064 287, 2687.13

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

Q: I also Need help with part D please

A: The correlation coefficient is 0.8137.

Q: Working is needed for this question.

A: Fact :- Two regions are adjacent if they share a common border.

Q: A car is traveling at 60 feet per second when the driver spots a deer in the road 300 feet ahead and…

A: Given, a car is traveling at 60 feet per second when the driver spots a deer in the road 300 feet…

Q: Find the values of x and y

A: in given right angle triangle as both side are equal it is isosceles right angle triangle

Q: Thank you so much

Q: Preliminary work Evaluate Vx? + 6x dr.

Q: 4. Find the domain and range of the given relation. State the domain and range as an inequality.…

Q: Use a= .05 and two tailed test t= 1.25, df = 40. reject, fail to reject

A: Given α = 0.05, two tailed test, t = 1.25 and degree of freedom = 40.For a two tail test if test…

Q: Your missing the part d solution

A: First three parts are as solved before.

Q: Can you add more detail for A

A: The given problem is to find the amount of glass is needed to make the entire container with the…

Q: A company institutes an exercise break for its workers to see the effect on job satisfaction, as…

A: Consider that µd is the true mean difference of worker job satisfaction after the implementation of…

Q: how do you calculate the t-value from the table. I'm confused

A: t value is based on sample size and level of significance. The t table given is for greater than…

Q: What's the probability that you made a Type I error? There is no Type I Error Half a percent OA…

A: Given Information: BMI of a five year old girl is 15. That is, the hypothesized value of population…

Q: Part D?

A: As per your instructions i have to solve part(D)

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

100%

Did I calculate this correctly? Thank you.

### Constructing a 95% Confidence Interval for Mean Monthly Salary

- **Problem Statement:**
The mean monthly salary of a random sample of 25 college graduates under the age of 35 was found to be $2425 with a standard deviation of $635. Assume that the distribution of monthly salaries for all college graduates under the age of 35 is approximately normally distributed. We need to construct a 95% confidence interval for the population mean of monthly salaries of all college graduates under the age of 35.

#### Given Data:
- Sample size ($ n $): 25
- Sample mean ($ \overline{X} $): $2425
- Standard deviation ($ s $): $635

#### Step-by-Step Solution:

1. **Determine the degrees of freedom (d.f.):**
\[
\text{d.f.} = n - 1 = 25 - 1 = 24
\]

2. **Find the critical value ($ t_c $) for a 95% confidence interval**
- From the $ t $-distribution table, for 24 degrees of freedom and a 95% confidence level, ($ \alpha/2 = 0.025 $), the critical value ($ t_c $) is approximately 2.064.

3. **Applying the formula for the confidence interval:**
\[
\overline{X} \pm t_c \left( \frac{s}{\sqrt{n}} \right)
\]

4. **Plugging in the values:**
\[
2425 \pm 2.064 \left( \frac{635}{\sqrt{25}} \right)
\]
\[
2425 \pm 2.064 \left( \frac{635}{5} \right)
\]
\[
2425 \pm 2.064 \times 127
\]
\[
2425 \pm 262.128
\]

5. **Calculate the intervals:**
\[
\text{Lower bound} = 2425 - 262.128 = 2162.872
\]
\[
\text{Upper bound} = 2425 + 262.128 = 2687.128
\]

#### Conclusion:
The 95% confidence interval for

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

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