The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth-grade students. Scores on the test range from 0 to 500. Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem-and-leaf plot.In 2015, 136,900 eighth-graders were in the NAEP sample for the mathematics test. The mean mathematics score was $ \bar{x} = 282 $. We want to estimate the mean score $ \mu $ in the population of all eighth-graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation $ \sigma = 110 $.(a) If we take many samples, the sample mean $ \bar{x} $ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score $ \mu $ in the population. What is the standard deviation of this sampling distribution? (Enter your answer rounded to four decimal places.)\[ \text{standard deviation} = \boxed{} \](b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of $ \bar{x} $ fall within how many points on either side of the unknown mean $ \mu $? (Enter your answer rounded to four decimal places.)\[ \text{points} = \boxed{} \] (c) What is the 95% confidence interval for the population mean score $ \mu $ based on this one sample? (Enter your answer rounded to one decimal place.)- Lower value = [Text box for response]- Higher value = [Text box for response]

The mean and standard deviation of the sampling distribution of the sample mean is equal to μXˉ and…

(a) If we take many samples, the sample mean i varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score µ in the population. What is the standard deviation of this sampling distribution? (Enter your answer rounded to four decimal places.)

(a) If we take many samples, the sample mean i varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score µ in the population. What is the standard deviation of this sampling distribution? (Enter your answer rounded to four decimal places.)

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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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

The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth-grade students. Scores on the test range from 0 to 500. Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem-and-leaf plot.

In 2015, 136,900 eighth-graders were in the NAEP sample for the mathematics test. The mean mathematics score was $ \bar{x} = 282 $. We want to estimate the mean score $ \mu $ in the population of all eighth-graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation $ \sigma = 110 $.

(a) If we take many samples, the sample mean $ \bar{x} $ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score $ \mu $ in the population. What is the standard deviation of this sampling distribution? (Enter your answer rounded to four decimal places.)

\[ \text{standard deviation} = \boxed{} \]

(b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of $ \bar{x} $ fall within how many points on either side of the unknown mean $ \mu $? (Enter your answer rounded to four decimal places.)

\[ \text{points} = \boxed{} \]

(c) What is the 95% confidence interval for the population mean score $ \mu $ based on this one sample? (Enter your answer rounded to one decimal place.)

- Lower value = [Text box for response]

- Higher value = [Text box for response]

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