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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

Expert verified

The test is left-tailed test

Step by step solution

01

Given Information

Archer's standard deviation of hits is 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 σ2=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, σ2<36is 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.

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Most popular questions from this chapter

The number of births per woman in China is 1.6down from 5.91in 1966. This fertility rate has been attributed to the law passed in 1979restricting births to one per woman. Suppose that a group of students studied whether or not the standard deviation of births per woman was greater than 0.75. They asked 50women across China the number of births they had had. The results are shown in Table. Does the students’ survey indicate that the standard deviation is greater than 0.75?

# of birthsFrequency0513021035

Refer back to the information in Try It. How many service providing jobs are there expected to be in 2020 ? How many nonagriculture wage and salary jobs are there expected to be in 2020?

Determine the appropriate test to be used in the next three exercises.

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Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. They are also interested in the variation of the number of babies. Suppose that an airline executive believes the average number of babies on flights is six with a variance of nine at most. The airline conducts a survey. The results of the 18 flights surveyed give a sample average of 6.4 with a sample standard deviation of 3.9. Conduct a hypothesis test of the airline executive’s belief.

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