Answered: Fran is training for her first…

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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Question

Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 34 randomly selected people who train in groups, and finds that they run a mean of 42.8 miles per week. Assume that the population standard deviation for group runners is known to be 3.8 miles per week. She also interviews a random sample of 41 people who train on their own and finds that they run a mean of 40.9 miles per week. Assume that the population standard deviation for people who run by themselves is 2.7miles per week. Test the claim at the 0.05 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2.

Step 1 of 3:

State the null and alternative hypotheses for the test. Fill in the blank below.

H0: μ1=μ2: Ha: μ1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯μ2

Compute the value of the test statistic. Round your answer to two decimal places.

Draw a conclusion and interpret the decision.

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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