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Chapter 11: Q4CQQ (page 533)

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

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

One Big Bill or Many Smaller Bills In a study of the 鈥渄enomination effect,鈥� 150 women in China were given either a single 100 yuan bill or a total of 100 yuan in smaller bills. The value of 100 yuan is about $15. The women were given the choice of spending the money on specific items or keeping the money. The results are summarized in the table below (based on 鈥淭he Denomination Effect,鈥� by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36). Use a 0.05 significance level to test the claim that the form of the 100 yuan is independent of whether the money was spent. What does the result suggest about a denomination effect?

Spent the Money

Kept the Money

Women Given a Single 100-Yuan Bill

60

15

Women Given 100 Yuan in Smaller Bills

68

7

Loaded Die The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 31, 42, 40, 28, and 32. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?

A study of people who refused to answer survey questions provided the randomly selected sample data shown in the table below (based on data from 鈥淚 Hear You Knocking But You Can鈥檛 Come In,鈥� by Fitzgerald and Fuller, Sociological Methods and Research,Vol. 11, No. 1). At the 0.01 significance level, test the claim that the cooperation of

the subject (response or refusal) is independent of the age category. Does any particular age group appear to be particularly uncooperative?

Age


18-21

22-29

30-39

40-49

50-59

60 and over

Responded

73

255

245

136

138

202

Refused

11

20

33

16

27

49

Do World War II Bomb Hits Fit a Poisson Distribution? In analyzing hits by V-1 buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25\(k{m^2}\). Shown below is a table of actual frequencies of hits and the frequencies expected with the Poisson distribution. (The Poisson distribution is described in Section 5-3.) Use the values listed and a 0.05 significance level to test the claim that the actual frequencies fit a Poisson distribution. Does the result prove that the data conform to the Poisson distribution?

Number of Bomb Hits

0

1

2

3

4

Actual Number of Regions

229

211

93

35

8

Expected Number of Regions

(from Poisson Distribution)

227.5

211.4

97.9

30.5

8.7

Is the hypothesis test described in Exercise 1 right tailed, left-tailed, or two-tailed? Explain your choice.
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