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Chapter 1: Q23E (page 27)

The article 鈥淪tatistical Modeling of the Time Courseof Tantrum Anger鈥� (Annals of Applied Stats, 2009:1013鈥�1034) discussed how anger intensity in children鈥檚 tantrums could be related to tantrumduration as well as behavioral indicators such asshouting, stamping, and pushing or pulling. The followingfrequency distribution was given (and also

the corresponding histogram):

0-<2: 136 2-<4: 92 4-<11: 71

11-<20: 26 20-<30: 7 30-<40: 3

Draw the histogram and then comment on any interesting features.

Short Answer

Expert verified

The histogram is represented as,

Step by step solution

01

Given information

The following data is given,

0-2

136

2-4

92

4-11

71

11-20

26

20-30

7

30-40

3

02

Construct a histogram and state its features

Steps to construct a histogram are,

1) Determine the frequency or the relative frequency.

2) Mark the class boundaries on the horizontal axis.

3) Draw a rectangle on the horizontal axis corresponding to the frequency or relative frequency.

The histogram is represented as,

From the above-diagram, it can be concluded that the histogram is unimodal and the distribution is positively skewed.

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Most popular questions from this chapter

Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaine-induced excited delirium (ED) and for a sample of those who had died from a cocaine overdose without excited delirium; survival time for people in both groups was at most 6 hours. The accompanying data was read from a comparative boxplot in the article 鈥淔atal Excited Delirium Following Cocaine Use鈥� (J.

of Forensic Sciences, 1997: 25鈥�31).

ED0 0 0 0 .1 .1 .1 .1 .2 .2 .3 .3

.3 .4 .5 .7 .8 1.0 1.5 2.7 2.8

3.5 4.0 8.9 9.2 11.7 21.0

Non-ED0 0 0 0 0 .1 .1 .1 .1 .2 .2 .2

.3 .3 .3 .4 .5 .5 .6 .8 .9 1.0

1.2 1.4 1.5 1.7 2.0 3.2 3.5 4.1

4.3 4.8 5.0 5.6 5.9 6.0 6.4 7.9

8.3 8.7 9.1 9.6 9.9 11.0 11.5

12.2 12.7 14.0 16.6 17.8

a. Determine the medians, fourths, and fourth spreads for the two samples.

b. Are there any outliers in either sample? Any extreme outliers?

c. Construct a comparative boxplot, and use it as a basis for comparing and contrasting the ED and non-ED samples.

A study carried out to investigate the distribution of total braking time (reaction time plus accelerator-to-brake movement time, in ms) during real driving conditions at 60 km/hr gave the following summary information on the distribution of times (鈥淎 Field Study on Braking Responses During Driving,鈥� Ergonomics, 1995: 1903鈥�1910):

mean= 535 median=500 mode=500

sd=96 minimum=220 maximum=925

5th percentile=400 10th percentile=430

90th percentile =640 95th percentile= 720

What can you conclude about the shape of a histogram of this data? Explain your reasoning.

Mercury is a persistent and dispersive environmental contaminantfound in many ecosystems around the world.When released as an industrial by-product, it often finds itsway into aquatic systems where it can have deleteriouseffects on various avian and aquatic species. The accompanyingdata on blood mercury concentration (mg/g) for adult

females near contaminated rivers in Virginia was read from a graph in the article 鈥淢ercury Exposure Effects the Reproductive Success of a Free-Living Terrestrial Songbird, the Carolina Wren鈥� (The Auk, 2011: 759鈥�769;this is a publication of the American Ornithologists鈥� Union).

.20 .22 .25 .30 .34 .41 .55 .56

1.42 1.70 1.83 2.20 2.25 3.07 3.25

a. Determine the values of the sample mean and sample median and explain why they are different. (Hint:\(\sum {{{\bf{x}}_{\bf{1}}}{\bf{ = 18}}{\bf{.55}}} \))

b. Determine the value of the 10% trimmed mean and compare to the mean and median.

c. By how much could the observation .20 be increased without impacting the value of the sample median?

a. Let aand bbe constants and let\({y_i} = a{x_i} + b\)fori=1, 2, . . . , n. What are the relationships between\(\bar x\)and\(\bar y\)and between\(s_x^2\)and\(s_y^2\)?

b. A sample of temperatures for initiating a certain chemical reaction yielded a sample average (掳C) of 87.3 and a sample standard deviation of 1.04. What are the sample average and standard deviation measured in 掳F? (Hint:\(F = \frac{9}{5}C + 32\))

A sample of n=10 automobiles was selected, and eachwas subjected to a 5-mph crash test. Denoting a car withno visible damage by S (for success) and a car with suchdamage by F, results were as follows:

S S F S SS F F S S

  1. What is the value of the sample proportion of successes x/n?
  2. Replace each S with a 1 and each F with a 0. Then calculate for this numerically coded sample. How does compare to x/n?
  3. Suppose it is decided to include 15 more cars in the experiment. How many of these would have to be S鈥檚 to give x/n = .80 for the entire sample of 25 cars?
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