/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q3BSC In Exercises 1鈥�4, use the foll... [FREE SOLUTION] | 91影视

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Chapter 11: Q3BSC (page 533)

In Exercises 1鈥�4, use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time.

Flight 1

-32

-25

-26

-6

5

-15

-17

-36

Flight 19

-5

-32

-13

-9

-19

49

-30

-23

Flight 21

-23

28

103

-19

-5

-46

13

-3

Test Statistic What is the value of the test statistic? What distribution is used with the test statistic?

Short Answer

Expert verified

The value of the test statistic is 1.334.

The test statistic follows F-distribution with (2,21) degrees of freedom.

Step by step solution

01

Given information

The output for ANOVA is given from SPSS.

02

Identify the value of test statistic

The value of the test statistic can be obtained from the SPSS output from the column header F.

Thus, the test statistic is 1.334, which is computed as follows:

\(\begin{array}{c}F = \frac{{{\rm{Mean}}\;{\rm{square}}\;{\rm{between}}\;{\rm{groups}}}}{{{\rm{Mean}}\;{\rm{square}}\;{\rm{within}}\;{\rm{groups}}}}\\ = \frac{{1287.500}}{{965.310}}\\ = 1.334\end{array}\)

Thus, the F-statistic is 1.334.

03

Identify the distribution of the test statistic

F-distribution describes the ratio of two variance measures.

The test statistic uses F-distribution, which has two degrees of freedom:

  • The numerator degrees of freedom, which is 2
  • The denominator degrees of freedom, which is 21.

Thus, the test statistic uses F-distribution with (2,21) degrees of freedom.

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Most popular questions from this chapter

Motor Vehicle Fatalities The table below lists motor vehicle fatalities by day of the week for a recent year (based on data from the Insurance Institute for Highway Safety). Use a 0.01 significance level to test the claim that auto fatalities occur on the different days of the week with the same frequency. Provide an explanation for the results.

Day

Sun.

Mon.

Tues.

Wed.

Thurs.

Fri.

Sat.

Frequency

5304

4002

4082

4010

4268

5068

5985

In Exercises 1鈥�4, use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time.

Flight 1

-32

-25

-26

-6

5

-15

-17

-36

Flight 19

-5

-32

-13

-9

-19

49

-30

-23

Flight 21

-23

28

103

-19

-5

-46

13

-3

P-Value If we use a 0.05 significance level in analysis of variance with the sample data given in Exercise 1, what is the P-value? What should we conclude? If a passenger abhors late flight arrivals, can that passenger be helped by selecting one of the flights?

Benford鈥檚 Law. According to Benford鈥檚 law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercises 21鈥�24, test for goodness-of-fit with the distribution described by Benford鈥檚 law.

Leading Digits

Benford's Law: Distributuon of leading digits

1

30.10%

2

17.60%

3

12.50%

4

9.70%

5

7.90%

6

6.70%

7

5.80%

8

5.10%

9

4.60%

Author鈥檚 Computer Files The author recorded the leading digits of the sizes of the electronic document files for the current edition of this book. The leading digits have frequencies of 55, 25, 17, 24, 18, 12, 12, 3, and 4 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively). Using a 0.05 significance level, test for goodness-of-fit with Benford鈥檚 law.

Benford鈥檚 Law. According to Benford鈥檚 law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercises 21鈥�24, test for goodness-of-fit with the distribution described by Benford鈥檚 law.

Leading Digits

Benford's Law: Distributuon of leading digits

1

30.10%

2

17.60%

3

12.50%

4

9.70%

5

7.90%

6

6.70%

7

5.80%

8

5.10%

9

4.60%

Tax Cheating? Frequencies of leading digits from IRS tax files are 152, 89, 63, 48, 39, 40, 28, 25, and 27 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively, based on data from Mark Nigrini, who provides software for Benford data analysis). Using a 0.05 significance level, test for goodness-of-fit with Benford鈥檚 law. Does it appear that the tax entries are legitimate?

Exercises 1鈥�5 refer to the sample data in the following table, which summarizes the last digits of the heights (cm) of 300 randomly selected subjects (from Data Set 1 鈥淏ody Data鈥� in Appendix B). Assume that we want to use a 0.05 significance level to test the claim that the data are from a population having the property that the last digits are all equally likely.

Last Digit

0

1

2

3

4

5

6

7

8

9

Frequency

30

35

24

25

35

36

37

27

27

24

Is the hypothesis test left-tailed, right-tailed, or two-tailed?
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