Research Question Is the typical US runner getting faster or slower over time? The average time for all runners who finished the Cherry Blossom Race in 2006 was 93.29 minutes (93 minutes and about 17 seconds). We want to determine using data from 100 participants in the 2017 Cherry Blossom Race whether runners in this race are getting faster or slower, versus the other possibility that there has been no change. a)What parameter are the researchers trying to learn more about? Choice 1:The mean finishing time for all runners in the 2017 race. Choice 2:The mean finishing time for the runners in our sample from 2017. Choice 3:The mean finishing time for all runners in the 2006 race. Choice 4:The proportion of all runners who finished the 2017 race in a time that was different than 93.29 minutes. b)What should we use for our null hypothesis? What should we use for our alternative hypothesis? c)Suppose we go out and take a random sample of 100 runners from the 2017 race. If the null hypothesis is true, what would you expect to be the (approximate) average time for these runners? Expected average time = d)Suppose we take a sample of 100 runners from the 2017 race, and find that the average finishing time is \bar{x} = 98.78xˉ=98.78 minutes, with a standard deviation of s = 16.59s=16.59 minutes. Using this data, what is our best estimate for the standard error of the sampling distribution for bar xˉ? SE = e)Find the test statistic for our hypothesis test. f)Find the P-value for this hypothesis test. g)What conclusions can we make at the α=0.05 significance level? Choice 1:Reject H_0in f avor of H_A Choice 2 of 2:Fail to reject H_0.

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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Research Question Is the typical US runner getting faster or slower over time?

The average time for all runners who finished the Cherry Blossom Race in 2006 was 93.29 minutes (93 minutes and about 17 seconds). We want to determine using data from 100 participants in the 2017 Cherry Blossom Race whether runners in this race are getting faster or slower, versus the other possibility that there has been no change.

a)What parameter are the researchers trying to learn more about?

Choice 1:The mean finishing time for all runners in the 2017 race.

Choice 2:The mean finishing time for the runners in our sample from 2017.

Choice 3:The mean finishing time for all runners in the 2006 race.

Choice 4:The proportion of all runners who finished the 2017 race in a time that was different than 93.29 minutes.

b)What should we use for our null hypothesis? What should we use for our alternative hypothesis?

c)Suppose we go out and take a random sample of 100 runners from the 2017 race. If the null hypothesis is true, what would you expect to be the (approximate) average time for these runners?

Expected average time =

d)Suppose we take a sample of 100 runners from the 2017 race, and find that the average finishing time is \bar{x} = 98.78xˉ=98.78 minutes, with a standard deviation of s = 16.59s=16.59 minutes.

Using this data, what is our best estimate for the standard error of the sampling distribution for bar xˉ?

SE =

e)Find the test statistic for our hypothesis test.

f)Find the P-value for this hypothesis test.

g)What conclusions can we make at the α=0.05 significance level?

Choice 1:Reject H_0in f avor of H_A

Choice 2 of 2:Fail to reject H_0.

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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