Most individuals are aware of the fact that the average annu

Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 20 automobiles 4 years old showed a sample standard deviation for annual repair costs of $170 and a sample of 21 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. Let 4 year old automobiles be represented by population 1. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles. SO the question asks me Ho:o1 squared then it says is greater than, greater than or equal to, equal to, less than or equal to, less than, not equal to. ( I have to select one of those for the answer) if you could do that please..... the next question is the exact same but it says Ha instead of Ho... Thanks!

Solution

Note that the claima always goes to the alternative hypothesis, so Ha: sigma1^2 > sigma2^2.

Also, the null hypothesis is the exact opposite of the alternative.

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 <= sigma2^2  
Ha:    sigma1^2 > sigma2^2   [ANSWER]