A new type of crank for bicycles called the Powercam relies on a pushing motion rather than a circularmotion. The company that markets this crank plans a test of five riders who will travel a 100-mileroute once with the Powercam and once with a conventional crank. The company claims that the newcrank reduces the time needed to cover the 100 miles. The times in hours for the five riders are asfollows:RiderPowercamConventional 5.1144.44.64.74.84.95.3 5.14.9 5.2Is there sufficient evidence in the data to support the claim that the new crank reduces the time neededto cover the 100 miles? Use a 5% significance level and assume that both population distributions arenormal.(a) State the null and alternative hypotheses for the test.(b) Identify the correct formula for the test statistic and calculate its value.(c) Identify the rejection region.(d) Make a decision whether to reject Ho.(e) State a conclusion in the context of the problem.

Given : Use a 5% significance level

A new type of crank for bicycles called the Powercam relies on a pushing motion rather than a circular motion. The company that markets this crank plans a test of five riders who will travel a 100-mile route once with the Powercam and once with a convetional crank. The company claims that the new crank reduces the time needed to cover the 100 miles. The times in hours for the five riders are as follows: 1 4.4 4.6 4.7 4.8 4.9 Rider 2 3 4 5 Powercam Conventional 5.1 5.3 5.1 4.9 5.2 Is there sufficient evidence in the data to support the claim that the new crank reduces the time needed to cover the 100 miles? Use a 5% significance level and assume that both population distributions are normal.

A new type of crank for bicycles called the Powercam relies on a pushing motion rather than a circular motion. The company that markets this crank plans a test of five riders who will travel a 100-mile route once with the Powercam and once with a convetional crank. The company claims that the new crank reduces the time needed to cover the 100 miles. The times in hours for the five riders are as follows: 1 4.4 4.6 4.7 4.8 4.9 Rider 2 3 4 5 Powercam Conventional 5.1 5.3 5.1 4.9 5.2 Is there sufficient evidence in the data to support the claim that the new crank reduces the time needed to cover the 100 miles? Use a 5% significance level and assume that both population distributions are normal.

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

A new type of crank for bicycles called the Powercam relies on a pushing motion rather than a circular
motion. The company that markets this crank plans a test of five riders who will travel a 100-mile
route once with the Powercam and once with a conventional crank. The company claims that the new
crank reduces the time needed to cover the 100 miles. The times in hours for the five riders are as
follows:
Rider
Powercam
Conventional 5.1
1
4
4.4
4.6
4.7
4.8
4.9
5.3 5.1
4.9 5.2
Is there sufficient evidence in the data to support the claim that the new crank reduces the time needed
to cover the 100 miles? Use a 5% significance level and assume that both population distributions are
normal.
(a) State the null and alternative hypotheses for the test.
(b) Identify the correct formula for the test statistic and calculate its value.
(c) Identify the rejection region.
(d) Make a decision whether to reject Ho.
(e) State a conclusion in the context of the problem.

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