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Chapter 11: Q11-2BSC (page 533)

Cybersecurity When using the data from Exercise 1 to test for goodness-of-fit with the distribution described by Benford鈥檚 law, identify the null and alternative hypotheses.

Short Answer

Expert verified

The null hypothesis and the alternative hypothesis is

\(\begin{aligned}{l}{H_0}:{p_1} = 0.301,{p_2} = 0.176,{p_3} = 0.125,{p_4} = 0.097,{p_5} = 0.079,{p_6} = 0.067,{p_7} = 0.058,\\\;\;\;\;\;{p_8} = 0.051,{p_9} = 0.046\end{aligned}\)

\({H_1}:\)At least one of the proportions will differ from the others.

Step by step solution

01

Given information

The observed frequencies and the expected frequencies of the leading digits of inter-arrival traffic times are tabulated.

02

Identify the hypotheses

The following hypotheses are set up to test for the goodness of fit test of the given distribution:

Null Hypothesis:

The null hypothesis is that in which the proportions of all the leading digits should be equal to the claimed value.

\(\begin{aligned}{l}{H_0}:{p_1} = 0.301,{p_2} = 0.176,{p_3} = 0.125,{p_4} = 0.097,{p_5} = 0.079,{p_6} = 0.067,{p_7} = 0.058,\\\;\;\;\;\;{p_8} = 0.051,{p_9} = 0.046\end{aligned}\)

Alternative Hypothesis:

The alternative hypothesis is that in which at least one of the proportions should not be equal to the claimed value.

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Most popular questions from this chapter

Questions 6鈥�10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.


Men

Women

Boys

Girls

Survived

332

318

29

27

Died

1360

104

35

18

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60

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Women Given 100 Yuan in Smaller Bills

68

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Flat Tire and Missed Class A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn鈥檛 have a flat tire, would they be able to identify the same tire? The author asked 41 other students to identify the tire they would select. The results are listed in the following table (except for one student who selected the spare). Use a 0.05 significance level to test the author鈥檚 claim that the results fit a uniform distribution. What does the result suggest about the likelihood of four students identifying the same tire when they really didn鈥檛 have a flat tire?

Tire

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Left Rear

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Number Selected

11

15

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16

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

Given that the P-value for the hypothesis test is 0.501, what do you conclude? Does it appear that the heights were obtained through measurement or that the subjects reported their heights?

Forward Grip Reach and Ergonomics When designing cars and aircraft, we must consider the forward grip reach of women. Women have normally distributed forward grip reaches with a mean of 686 mm and a standard deviation of 34 mm (based on anthropometric survey data from Gordon, Churchill, et al.).

a. If a car dashboard is positioned so that it can be reached by 95% of women, what is the shortest forward grip reach that can access the dashboard?

b. If a car dashboard is positioned so that it can be reached by women with a grip reach greater than 650 mm, what percentage of women cannot reach the dashboard? Is that percentage too high?

c. Find the probability that 16 randomly selected women have forward grip reaches with a mean greater than 680 mm. Does this result have any effect on the design?
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