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Chapter 11: Q 60 (page 658)

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

Expert verified

Null hypothesis: 蟽2=36

Alternative hypothesis:蟽2<36

Step by step solution

01

Given Information

Archer's standard deviation of hits 6

Observer's claim is standard deviation is less than 6

02

Explanation

From the provided data the archer's standard deviation is six. Therefore the variance should be62=36. Therefore the null hypothesis is蟽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.蟽2<36

.

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