Question

Test of a Single Variance

Use the following information to answer the next three exercises: An archer's standard deviation for his hits is six (data is measured in distance from the center of the target). An observer claims the standard deviation is less. 60. State the null and alternative hypotheses.

Short answer

Null hypothesis: ${\sigma }^2=36$

Alternative hypothesis:${\sigma }^2<36$

Step-by-step solution

Given Information

Archer's standard deviation of hits 6

Observer's claim is standard deviation is less than 6

Explanation

From the provided data the archer's standard deviation is six. Therefore the variance should be$6^2=36$. Therefore the null hypothesis is${\sigma }^2=36$

But the observer claims that the standard deviation is less than six. Consequently, the variance for that is less than 36. Hence the alternative hypothesis is.${\sigma }^2<36$

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