You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:\[ 65.4, \, 20.7, \, 56.3, \, 14.8, \, 29.5, \, 12.6, \, 27.4, \, 40.6, \, 17.6, \, 36.3 \]Find the 90% 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.\[ \text{90% C.I.} = \, \_\_\_\_ \]

The sample mean is, x¯=∑iXn=65.4+20.7+56.3+14.8+29.5+12.6+27.4+40.6+17.6+36.310=321.210=32.12 The…

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

\[ 65.4, \, 20.7, \, 56.3, \, 14.8, \, 29.5, \, 12.6, \, 27.4, \, 40.6, \, 17.6, \, 36.3 \]

Find the 90% 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.

\[ \text{90% C.I.} = \, \_\_\_\_ \]

Expert Solution

Step 1

The sample mean is,

$\begin{array}{rcl} \bar{x} & = & \frac{\sum_{i} X}{n} \\ = & \frac{65.4 + 20.7 + 56.3 + 14.8 + 29.5 + 12.6 + 27.4 + 40.6 + 17.6 + 36.3}{10} \\ = & \frac{321.2}{10} \\ = & 32.12 \end{array}$

The sample mean is 32.12.

The sample standard deviation is,

$\begin{array}{rcl} s & = & \sqrt{\frac{\sum_{i} {(X - \bar{x})}^{2}}{n - 1}} \\ = & \sqrt{\frac{{(65.4 - 32.12)}^{2} + {(20.7 - 32.12)}^{2} + {(56.3 - 32.12)}^{2} + {(14.8 - 32.12)}^{2} + {(29.5 - 32.12)}^{2} + {(12.6 - 32.12)}^{2} + {(27.4 - 32.12)}^{2} + {(40.6 - 32.12)}^{2} + {(17.6 - 32.12)}^{2} + {(36.3 - 32.12)}^{2}}{10 - 1}} \\ = & \sqrt{\frac{2833.0160}{9}} \\ = & \sqrt{314.7796} \\ = & 17.7420 \end{array}$

The sample standard deviation is 17.7420.

The degrees of freedom is,

$\begin{array}{rcl} d f & = & n - 1 \\ = & 10 - 1 \\ = & 9 \end{array}$

The degrees of freedom is 9.

The confidence level is 90%, then the level of significance is 0.10.

Computation of critical value:

The critical value of t-distribution at 9 degrees of freedom can be obtained using the excel formula “=T.INV.2T(0.10,9)”. The critical value is 1.8331.

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