Suppose the math department chair at a large state university wants to estimate the average overall rating, out of five points, that students taking Introductory Statistics gave their lecturers on their end-of-term evaluations. She selects a random sample of 38 evaluations and records the summary statistics shown. | Sample size (n) | Sample mean ($ \bar{x} $) | Sample standard deviation (s) | Population standard deviation ($ \sigma $) | Standard error ($ \sigma_{\bar{x}} $) | Confidence level (C) ||-----------------|-----------------------------|-------------------------------|-----------------------------------------------|----------------------------------------|---------------------|| 38 | 4.0414 | 1.0501 | 0.9903 | 0.1606 | 90% |The department chair determines the standard error using $ \sigma $, the standard deviation calculated from all student evaluations submitted to her department. Assume the Statistics lecturers' ratings have the same standard deviation.Use this information to find the margin of error and the lower and upper bounds of a 90% confidence interval for $ \mu $, the mean overall rating students gave their Introductory Statistics lecturers. Round your answers to the nearest hundredth.- Margin of error = [ ]- Lower bound = [ ]- Upper bound = [ ]Complete the following sentence to state the interpretation of the department chair's confidence interval.The ____________________ that the ____________________ of the overall ratings given on ____________________. ### Educational Website Text Transcription**Margin of error =** [ ]**Lower bound =** [ ] **Upper bound =** [ ]Complete the following sentence to state the interpretation of the department chair's confidence interval.The [ ____ ] that the [ ____ ] of the overall ratings given on [ ____ ] at the end of the term [ ____ ].### Answer Bank:- is 4.0414- the student evaluations in the sample- mean- confidence interval- probability is 90%- department chair is 90% confident- standard deviation- is between the lower and upper bounds- all student evaluations of Statistics lecturers- standard error### Instructions:Use the answer bank to fill in the blanks in the sentence to correctly interpret the department chair's confidence interval. Ensure all calculations are rounded to the nearest hundredth where applicable.

Since, standard deviation is known the critical value at 90% confidence level from the standard normal table will be: The margin of the error can be calculated as: Thus margin of error is 0.264The 90% confidence interval can be calculated as: Thus, Lower Bond = 3.777 Upper Bond = 4.305The confidence interval tells the probability and the range of value in which the population parameter which is the average overall rating of all the students in this case lies. Thus, the correct interpretation is : The department chair is 90% confident that the mean of the overall rating given on all student evaluations of Student lectures at the end of the term is between the lower and upper bounds.

Math

Statistics

Suppose the math department chair at a large state university wants to estimate the average overall rating, out of five points, that students taking Introductory Statistics gave their lecturers on their end-of-term evaluations. She selects a random samp. of 38 evaluations and records the summary statistics shown. Sample Sample Sample standard Population standard Standard Confidence size mean deviation deviation error level 38 4.0414 1.0501 0.9903 0.1606 90% The department chair determines the standard error using ơ, the standard deviation calculated from all student evaluations submitted to her department. Assume the Stațtistics lecturers' ratings have the same standard deviation. Use this information to find the margin of error and the lower and upper bounds of a 90% confidence interval for u, the mean overall rating students gave their Introductory Statistics lecturers. Round your answers to the nearest hundredth.

Suppose the math department chair at a large state university wants to estimate the average overall rating, out of five points, that students taking Introductory Statistics gave their lecturers on their end-of-term evaluations. She selects a random samp. of 38 evaluations and records the summary statistics shown. Sample Sample Sample standard Population standard Standard Confidence size mean deviation deviation error level 38 4.0414 1.0501 0.9903 0.1606 90% The department chair determines the standard error using ơ, the standard deviation calculated from all student evaluations submitted to her department. Assume the Stațtistics lecturers' ratings have the same standard deviation. Use this information to find the margin of error and the lower and upper bounds of a 90% confidence interval for u, the mean overall rating students gave their Introductory Statistics lecturers. Round your answers to the nearest hundredth.

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Suppose the math department chair at a large state university wants to estimate the average overall rating, out of five points, that students taking Introductory Statistics gave their lecturers on their end-of-term evaluations. She selects a random sample of 38 evaluations and records the summary statistics shown.

| Sample size (n) | Sample mean ($ \bar{x} $) | Sample standard deviation (s) | Population standard deviation ($ \sigma $) | Standard error ($ \sigma_{\bar{x}} $) | Confidence level (C) |
|-----------------|-----------------------------|-------------------------------|-----------------------------------------------|----------------------------------------|---------------------|
| 38 | 4.0414 | 1.0501 | 0.9903 | 0.1606 | 90% |

The department chair determines the standard error using $ \sigma $, the standard deviation calculated from all student evaluations submitted to her department. Assume the Statistics lecturers' ratings have the same standard deviation.

Use this information to find the margin of error and the lower and upper bounds of a 90% confidence interval for $ \mu $, the mean overall rating students gave their Introductory Statistics lecturers. Round your answers to the nearest hundredth.

- Margin of error = [ ]
- Lower bound = [ ]
- Upper bound = [ ]

Complete the following sentence to state the interpretation of the department chair's confidence interval.

The ____________________ that the ____________________ of the overall ratings given on ____________________.

### Educational Website Text Transcription

**Margin of error =** [ ]

**Lower bound =** [ ] **Upper bound =** [ ]

Complete the following sentence to state the interpretation of the department chair's confidence interval.

The [ ____ ] that the [ ____ ] of the overall ratings given on [ ____ ] at the end of the term [ ____ ].

### Answer Bank:
- is 4.0414
- the student evaluations in the sample
- mean
- confidence interval
- probability is 90%
- department chair is 90% confident
- standard deviation
- is between the lower and upper bounds
- all student evaluations of Statistics lecturers
- standard error

### Instructions:
Use the answer bank to fill in the blanks in the sentence to correctly interpret the department chair's confidence interval. Ensure all calculations are rounded to the nearest hundredth where applicable.

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