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.

Is this a right-tailed, left-tailed, or two-tailed test?

Short answer

The test is left-tailed test

Step-by-step solution

Given Information

Archer's standard deviation of hits is 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 ${\sigma }^2=36$

However, according to the observer, the standard deviation is less than six. As a result, the variance, in that case, is less than 36. As a result, ${\sigma }^2<36$is the alternate hypothesis.

The area under the curve indicates that the distribution is left-tailed when the normal distribution is drawn and the variance is 36 or less.