Question

State the null and alternative hypotheses.

Short answer

The null hypotheses is $H_0:{\sigma }_1={\sigma }_2$or ${\sigma }_1^2={\sigma }_2^2$and the alternative hypotheses is $H_1:{\sigma }_1<{\sigma }_2$ or ${\sigma }_1^2<{\sigma }_2^2$.

Step-by-step solution

Concept introduction

Hypothesis in statistics is defined as the report concerning the nature of a population. And it is usually expressed in terms of a population parameter.

Explanation

The null hypothesis is a statistical theory that states that no statistical link or significance exists between two collections of observational data and measured events in a given single observed variable.

Here, there is no significance difference between the cyclist records is given as below:
$H_0:{\sigma }_1={\sigma }_2$or ${\sigma }_1^2={\sigma }_2^2$
The alternative hypothesis is one of the hypothesis test's offered propositions in statistical hypothesis testing.

Therefore, the alternate hypothesis against the null hypothesis is given as:
$H_1:{\sigma }_1<{\sigma }_2$or ${\sigma }_1^2<{\sigma }_2^2$