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Chapter 11: Q 61 (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.

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 蟽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, 蟽2<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

In 2007, the United States had 1.5 million homeschooled students, according to the U.S. National Center for Education Statistics. In Table 11.56 you can see that parents decide to homeschool their children for different reasons, and some reasons are ranked by parents as more important than others. According to the survey results shown in the table, is the distribution of applicable reasons the same as the distribution of the most important reason? Provide your assessment at the

5% significance level. Did you expect the result you obtained?

Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distribution of their expected majors.

Major Women -Expected MajorWome -Actual Major
Arts & Humaities 14.0% 670
Biological Sciences
 8.4% 410
Business
 13.1% 685
Education 13.0% 650
Engineering
 2.6% 145
Physical Sciences
 2.6% 125
Professional
 18.9% 975
Social Sciences
 13.0% 605
Technical
 0.4% 15
Other
 5.8% 300
Undecided 8.0% 420

A sample standard deviation of 15minutes is the same as a sample variance of __________ minutes.

A six-sided die is rolled 120times. Fill in the expected frequency column. Then, conduct a hypothesis test to determine if the die is fair. The data in Table 11.34are the result of the 120rolls.

Face Value FrequencyExpected Frequency
115
229
316
415
530
615

In general, if the observed values and expected values of a goodness-of-fit test are not close together, then the test statistic can get very large and on a graph will be way out in the right tail.
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