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Name: You are given the sample of the population standard deviation use this
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Description: You are given the sample of the population standard deviation use this information to construct the 90% and 95% confidence interval for the population mean. Interpret the result and compare the width you the confidence intervals from a random sample

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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You are given the sample of the population standard deviation use this information to construct the 90% and 95% confidence interval for the population mean. Interpret the result and compare the width you the confidence intervals from a random sample of 57 dates, the mean record high daily temptin a certain city has a mean of 86.90F assume the population standard deviation is 15.39F

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 + ...

Expert Solution

Step 1

Solution:

Let X be the high daily tempt in a city.

From the given information, x-bar=86.90, σ=15.39 and n=57.

Step 2

The confidence level is 0.90.

Then, the 90% confidence interval for the population mean is

Then, the 90% confidence interval for the population mean is (83.5467, 90.2533).

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