Q.6 - The Practice of Statistics for AP

Question

When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be

 $\sigma$ = $10$ meters. An experienced jumper thinks that the organizers are underestimating the variation.

Step-by-Step Solution

Answer

Standard deviation is $10$ as per null hypothesis and is greater than $10$ as per alternative hypothesis.

Step 1: introduction

Given,

For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be $\sigma =10$ meters.

The null and alternative hypotheses are calculated.

Step 2: explanation

Standard devitaion is $\sigma =10$

Standard deviation is$10$as per null hypothesis  

 $\Rightarrow H_0:\sigma =10$

Standard deviation  is greater than $10$ as per alternative hypothesis

$\Rightarrow H_a:\sigma >10$

Standard deviation is $10$ as per null hypothesis and is greater than $10$ as per alternative hypothesis.