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If you are a dog lover, having your dog with you may reduce your stress level. Does having a friend with you reduce stress? To examine the effect of pets and friends in stressful situations, researchers recruited 45 women who said they were dog lovers. Fifteen women were assigned at random to each of three groups: to do a stressful task alone, with a good friend present, or with their dogs present. The stressful task was to count backward by 13s or 17s. The woman's average heart rate during the task was one measure of the effect of stress. The table below shows the data. Pet 58 64 65 68 69 69 69 70 70 72 76 79 85 86 99 Erlento BOSTE STR88800192 87888 12 072702 Alone 62 70 73 75 77 80 84 84 84 87 87 87 90 91 99
1. Use the rule to show that 99 is an outlier for the Pet group.

2. Use the applet to make parallel boxplots to compare the heart rates in the three groups.​

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MrRoyal

The outlier of a dataset is a data element that is relatively far from the remaining data elements

  • 99 is an outlier of pet group
  • See attachment for the parallel box plots

(a) Prove that 99 is an outlier for Pet

We have:

Pets: 58 64 65 68 69 69 69 70 70 72 76 79 85 86 99

[tex]n = 15[/tex]

The quartiles positions are:

[tex]Q_1 = \frac{n + 1}{4}[/tex]

[tex]Q_1 = \frac{15 + 1}{4}[/tex]

[tex]Q_1 = \frac{16}{4}[/tex]

[tex]Q_1 = 4th[/tex]

[tex]Q_3 = Q_1 \times 3[/tex]

[tex]Q_3 = 4th \times 3[/tex]

[tex]Q_3 = 12th[/tex]

So, we have:

[tex]Q_1 = 4th[/tex]

[tex]Q_3 = 12th[/tex]

From the pet group:

The data elements at the 4th and 12th positions are 68 and 79

So, we have:

[tex]Q_1 = 68[/tex]

[tex]Q_3= 79[/tex]

The lower and upper limits of the outlier are:

[tex]L = Q_1 - 1.5 \times (Q_3 - Q_1)[/tex]

[tex]U = Q_3 + 1.5 \times (Q_3 - Q_1)[/tex]

So, we have:

[tex]L = 68 - 1.5 \times (79 - 68)[/tex]

[tex]L = 51.5[/tex]

[tex]U = 79+ 1.5 \times (79 - 68)[/tex]

[tex]U = 95.5[/tex]

This means that data below 51.5 or above 95.5 are outliers.

Hence, 99 is an outlier because 99 is greater than 95.5

(b) The parallel box plot

The three groups are:

Pets: 58 64 65 68 69 69 69 70 70 72 76 79 85 86 99

Erlento: 88 80 80 81 92 87 88 81 82 80 87 92 87 80 82

Alone: 62 70 73 75 77 80 84 84 84 87 87 87 90 91 99

See attachment for the parallel box plots

Read more about box plots and outliers at:

https://brainly.com/question/14940764

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