A car company conducts crash tests of its new airbag system to evaluate its safety. One  hundred cars are run into a solid concrete barrier at a speed of 35 miles per hour, and  the chest compression of a crash test dummy is measured each time. They hope that  the average compression if the test were repeated over and over (which we could think  of as the population) would be about 2 inches, corresponding to an injury that would be  painful but not fatal. In the hundred tests, the average chest compression in the crash  test dummies was 2.1 inches, with an SD of 0.2 inches. (a) State the null and alternative hypotheses in terms of the problem. (b) What kind of box model will we use for this problem? A 0-1 box, or a box with other  values on the tickets? (c) State the null and alternative hypotheses in terms of the box model (d) Compute the z test statistic and the p-value, using the sample average as your  statistic as you compute z (e) What do you conclude?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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A car company conducts crash tests of its new airbag system to evaluate its safety. One 
hundred cars are run into a solid concrete barrier at a speed of 35 miles per hour, and 
the chest compression of a crash test dummy is measured each time. They hope that 
the average compression if the test were repeated over and over (which we could think 
of as the population) would be about 2 inches, corresponding to an injury that would be 
painful but not fatal. In the hundred tests, the average chest compression in the crash 
test dummies was 2.1 inches, with an SD of 0.2 inches.
(a) State the null and alternative hypotheses in terms of the problem.
(b) What kind of box model will we use for this problem? A 0-1 box, or a box with other 
values on the tickets?
(c) State the null and alternative hypotheses in terms of the box model

(d) Compute the z test statistic and the p-value, using the sample average as your 
statistic as you compute z

(e) What do you conclude?

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