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Description: A study is conducted to determine whether there is a difference in the mean scores of Collin County residents and Denton County residents on the state driver's license exam. The appropriate test is run on sample data and P = 0.0342. Select the corre

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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A study is conducted to determine whether there is a difference in the mean scores of Collin County residents and Denton County residents on the state driver's license exam. The appropriate test is run on sample data and P = 0.0342. Select the correct conclusion at the 0.05 level of significance.

Group of answer choices

Reject the null hypothesis; the evidence doe not support there is a significant difference in the means.

Reject the null hypothesis; the evidence supports there is a significant difference in the means.

Do not reject the null hypothesis; the evidence supports there is a significant difference in the means.

Do not reject the null hypothesis; the evidence does not support there is a significant difference in the means.

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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 Information:

A study is conducted to determine whether there is a difference in the mean scores of Collin County residents and Denton County residents on the state driver's license exam.

Hypothesis for this test would be as follows:

Null Hypothesis $H_{0} : μ_{1} = μ_{2}$ i.e., there is no significant difference between the mean scores of Collin County residents and Denton County residents on the state driver's license exam.

Alternative Hypothesis $H_{1} : μ_{1} \neq μ_{2}$ i.e., there is a significant difference between the mean scores of Collin County residents and Denton County residents on the state driver's license exam.

Now, p-value = 0.0342 and significance level $α$ = 0.05

Decision Rule:

If p-value is less than the significance level, reject the null hypothesis.

If p-value is greater than the significance level, we fail to reject the null hypothesis.

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