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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 ฯƒ2=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, ฯƒ2<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

You want to buy a specific computer. A sales representative of the manufacturer claims that retail stores sell this computer at an average price of \(1,249 with a very narrow standard deviation of \)25. You find a website that has a price comparison for the same computer at a series of stores as follows: \(1,299;\)1,229.99;\(1,193.08;\)1,279;\(1,224.95;\)1,229.99;\(1,269.95;\)1,249. Can you argue that pricing has a larger standard deviation than claimed by the manufacturer? Use the 5% significance level. As a potential buyer, what would be the practical conclusion from your analysis?

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

An archeologist is calculating the distribution of the frequency of the number of artifacts she finds in a dig site. Based on

previous digs, the archeologist creates an expected distribution broken down by grid sections in the dig site. Once the site has been fully excavated, she compares the actual number of artifacts found in each grid section to see if her expectation was accurate.

Some travel agents claim that honeymoon hot spots vary according to the age of the bride. Suppose that 280recent brides were interviewed as to where they spent their honeymoons. The information is given in Table 11.46. Conduct a test of independence

Location20-2930-3940-4950and over
Niagara Falls15252520
Poconos15252510
Europe1025155
Virgin Islands2025155

A fisherman is interested in whether the distribution of fish caught in Green Valley Lake is the same as the distribution of fish caught in Echo Lake. Of the 191 randomly selected fish caught in Green Valley Lake, 105 were rainbow trout, 27 were other trout, 35 were bass, and 24 were catfish. Of the 293 randomly selected fish caught in Echo Lake, 115 were rainbow trout, 58 were other trout, 67 were bass, and 53 were catfish. Perform a test for homogeneity at a 5% level of significance.

If df=2, the chi-square distribution has a shape that reminds us of the exponential.

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