Answered: 2. Imagine the daily high temperature…

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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2. Imagine the daily high temperature in Toronto was recorded every day for 14 days in January, and the average of these temperatures is –3.0°C with a standard deviation of 3.5°C.

a) Calculate an 80% confidence interval for the mean assuming all necessary conditions hold. Interpret the confidence interval you computed. Round your final answer to two decimal places.

b) Explain the meaning of confidence intervals. How would your confidence level change if you accidentally used a wider margin of error? Explain.

c) In the 14 days, the range of the maximum daily temperature was -5°C to 8°C. Recall that the average was –3.0°C. What are the possible implications for the interval you calculated in part (a)?

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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