Answered: You are interested in finding a 90%…

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 CI Mean

You are interested in finding a 90% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 10 randomly selected non-residential college students. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t z distribution.

b. With 98% confidence the population mean minutes of concentration is between ____ and ____ minutes.

c. If many groups of 103 randomly selected members are studied, then a different confidence interval would be produced from each group. About____ percent of these confidence intervals will contain the true population mean minutes of concentration and about ____ percent will not contain the true population mean minutes of concentration.

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

Given that,

Sample size $n = 10$

Sample mean $\bar{x} = 16.6$

Sample standard deviation $s = 6.9474$

Step 2

a. To compute the confidence interval use a t distribution.

b. 90% confidence interval for the average commute that non-residential students have to their college:

Critical value:

The two tailed t critical value at 9 degrees of freedom and 90% confidence level is 1.8331.

Calculation:

The 90% confidence interval for the average commute that non-residential students have to their college can be calculated as follows:

$\begin{array}{rcl} C I & = & \bar{x} \pm t_{c} (\frac{s}{\sqrt{n}}) \\ = & 16.6 \pm 1.8331 (\frac{6.9474}{\sqrt{10}}) \\ = & 16.6 \pm 4.02725 \\ = & (12.573, 20.627) \end{array}$

The 90% confidence interval for the average commute that non-residential students have to their college is between 12.573 and 20.627.

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