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Chapter 11: Q.118 (page 668)

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

How did you know to test the variance instead of the mean?

Short Answer

Expert verified

From the claim, it is evident that researchers are tested for variance not for mean that the claim is the variance is no more than 150minutes.

Step by step solution

01

Given information

Given in the question that

A disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

02

Solution

The word variance directs to a statistical measurement of the distance between numerals in a data set. More precisely, variance measures how far each number in the set is from the mean and therefore from every additional number in the set. Variance is frequently showed by this symbol: σ2. It is used by both analysts and vendors to select volatility and market security.

So here the claim will be variance is not more than the 150

Thus it means that the researchers are tested for variance, not for the mean.

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Most popular questions from this chapter

Where is μlocated on a chi-square curve?

A meteorologist wants to know if East and West Australia have the same distribution of storms. What type of test should she use?

The expected percentage of the number of pets students have in their homes is distributed (this is the given distribution for the student population of the United States) as in Table 11.12.

Number of PetsPercent0181252303184+9

A random sample of 1,000students from the Eastern United States resulted in the data in Table 11.13.

Number of PetsFrequency02101240232031404+90

At the 1% significance level, does it appear that the distribution “number of pets” of students in the Eastern United States is different from the distribution for the United States student population as a whole? What is the p-value?

A sample of 212commercial businesses was surveyed for recycling one commodity; a commodity here means any one type of recyclable material such as plastic or aluminum. Table 11.41shows the business categories in the survey, the sample size of each category, and the number of businesses in each category that recycle one commodity. Based on the study, on average half of the businesses were expected to be recycling one commodity. As a result, the last column shows the expected number of businesses in each category that recycle one commodity. At the 5% significance level, perform a hypothesis test to determine if the observed number of businesses that recycle one commodity follows the uniform distribution of the expected values.

Business
Type		Number in
class		Observed Number that recycles one commodityExpected number that recycles one commodity
office35
19
17.5
Retail/
Wholesale		48
27
24
Food/
Restaurants		53
35
26.5
Manufacturing/
Medical		52
21
26
Hotel/Mixed24
9
12

Table 11.41

Use a solution sheet to solve the hypothesis test problem. Go to Appendix E for the chi-square solution sheet. Round expected frequency to two decimal places.

A recent debate about where in the United States skiers believe the skiing is best prompted the following survey. Test to see if the best ski area is independent of the level of the skier.

U.S. Ski AreaBeginnerIntermediateAdvanced
Tahoe203040
Utah10
3060
Colorado1040 50

Table11.43
See all solutions

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