Answered: You must estimate the mean 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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Related questions

Question

You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:

81.7

76.9

71.2

99.4

78.9

64.2

98.1

71.4

108.3

Find the 80% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.

80% C.I. = ______

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

$Given data is 81.7, 76.9, 71.2, 99.4, 78.9, 64.2, 98.1, 71.4, 108.3, Mean (\bar{x}) = \frac{sum of the data set}{total no . of data set} Mean (\bar{x}) = \frac{81.7 + 76.9 + 71.2 + 99.4 + 78.9 + 64.2 + 98.1 + 71.4 + 108.3}{9} Mean (\bar{x}) = 83.344 standard deviation (s) = \sqrt{\frac{\sum_{}^{} {(x - x)}^{2}}{n - 1}} s = \sqrt{\frac{{(81.9 - 83.344)}^{2} + {(76.9 - 83.344)}^{2} + {(71.2 - 83.344)}^{2} + {(99.4 - 83.344)}^{2} + {(78.9 - 83.344)}^{2} + {(64.2 - 83.344)}^{2} + {(98.1 - 83.344)}^{2} + {(71.4 - 83.344)}^{2} + {(81.9 - 83.344)}^{2} + {(108.3 - 83.344)}^{2}}{9 - 1}} s = 15.079$