Construct a 90% confidence interval of the population mean age for the college students in Example #5 with the sample size increased to 30 students. Compare your answer with Example #5 (picture).a. Identify n, x̅, ?, and zc, and find E.b. Find the left and right endpoints of the confidence interval.c. Interpret the results and compare them with Example #5. EXAMPLE #5Problem: A college admissions director wishes to estimate the mean age ofall students currently enrolled. In a random sample of 20 students, the meanage is found to be 22.9 years. From past studies, the standard deviation isknown to be 1.5 years, and the population is normally distributed. Constructa 90% confidence interval of the population mean age.Solution: Using n = 20, x ,22.9 = = 1.5, andZc = 1.645, the margin of error at the 90% confidence1.5√20σlevel is E= Zc-1.645= .≈ 0.6.42

We have to find a...n , x̄, zc and E b. Find the left and right endpoints of the confidence…

Answered: Construct a 90% confidence interval of…

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

Construct a 90% confidence interval of the population mean age for the college students in Example #5 with the sample size increased to 30 students. Compare your answer with Example #5 (picture).

a. Identify n, x̅, ?, and z_c, and find E.
b. Find the left and right endpoints of the confidence interval.
c. Interpret the results and compare them with Example #5.

EXAMPLE #5
Problem: A college admissions director wishes to estimate the mean age of
all students currently enrolled. In a random sample of 20 students, the mean
age is found to be 22.9 years. From past studies, the standard deviation is
known to be 1.5 years, and the population is normally distributed. Construct
a 90% confidence interval of the population mean age.
Solution: Using n = 20, x ,22.9 = = 1.5, and
Zc = 1.645, the margin of error at the 90% confidence
1.5
√20
σ
level is E= Zc-
1.645= .
≈ 0.6.
42

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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