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Chapter 11: Q4CQQ (page 533)

Exercises 1–5 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 “Body Data” 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

If using a 0.05 significance level to test the stated claim, find the number of degrees of freedom.

Short Answer

Expert verified

The degrees of freedom for the given test are equal to 9.

Step by step solution

01

Given information

The last digits of the heights of a sample of people are tabulated along with their respective frequencies.

02

Degrees of freedom

The degrees of freedom for the goodness of fit test has the following formula:

\(df = k - 1\)

Where k is the number of categories.

Here, the hypothesis test to test the claim that the given digits occur equally frequently is a goodness of fit test.

k denotes the number of last digits equal to 10.

The degrees of freedom are computed as shown:

\(\begin{aligned}{c}df = k - 1\\ = 10 - 1\\ = 9\end{aligned}\)

Thus, the degrees of freedom for the given test are equal to 9.

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Most popular questions from this chapter

Exercises 1–5 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 “Body Data” 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

What are the null and alternative hypotheses corresponding to the stated claim?

The accompanying table is from a study conducted

with the stated objective of addressing cell phone safety by understanding why we use a particular ear for cell phone use. (See “Hemispheric Dominance and Cell Phone Use,” by Seidman, Siegel, Shah, and Bowyer, JAMA Otolaryngology—Head & Neck Surgery,Vol. 139, No. 5.)

The goal was to determine whether the ear choice is associated with auditory or language brain hemispheric dominance. Assume that we want to test the claim that handedness and cell phone ear preference are independent of each other.

a. Use the data in the table to find the expected value for the cell that has an observed frequency of 3. Round the result to three decimal places.

b. What does the expected value indicate about the requirements for the hypothesis test?

Right Ear

Left Ear

No Preference

Right-Handed

436

166

40

Left-Handed

16

50

3

Questions 6–10 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

Identify the null and alternative hypotheses corresponding to the stated claim.

Cybersecurity What do the results from the preceding exercises suggest about the possibility that the computer has been hacked? Is there any corrective action that should be taken?

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
See all solutions

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