Answered: The ?� confidence interval and test are…

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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Question

The ?� confidence interval and test are based on the sampling distribution of the sample mean ?⎯⎯⎯.�¯. The National Survey of Student Engagement (NSSE) asks college seniors to rate how much their experience at their institution has contributed to their ability to analyze numerical and statistical information. Ratings are on a scale of 11 to 7,7, with 77 being the highest (best) rating. Suppose scores for all seniors in 2019 are Normal with mean ?=2.9 and standard deviation ?=1.0.. (The ratings take on integer values from 11 to 7,7, so the population of the ratings of all college seniors could not be normal. However, it is reasonable to assume that the sample mean ?⎯⎯⎯�¯ is approximately Normal, and it is the Normality of the sample mean that makes the use of ?� procedures reasonably accurate.)

You take an SRS of 100100 seniors. According to the 99.799.7 part of the 68-95-99.768-95-99.7 rule, about what range of ratings do you expect to see in your sample? Note that NSSE scores cannot be negative. Give your answers to one decimal place.

lower bound:

upper bound:

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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