Question

1.17 A study of the effects of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it takes to fall asleep. These data are obtained: Smokers: 69.3 56.0 22.1 47.6 53.2 48.1 52.7 34.4 60.2 43.8 23.2 13.8 Nonsmokers: 28.6 25.1 26.4 34.9 29.8 28.4 38.5 30.2 30.6 31.8 41.6 21.1 36.0 37.9 13.9 (a) Find the sample mean for each group. (b) Find the sample standard deviation for each group. (c) Make a dot plot of the data sets A and B on the same line. (d) Comment on what kind of impact smoking appears to have on the time required to fall asleep.

Answer 1

Answer:

a.

$\bar X_F=43.7$

$\bar X_{NF}=30.32$

b.

$S_F=16.9278$

$S_{NF}=7.12783$

c.

Attached file

d.

Apparently the practice of smoking reduces the ability to fall asleep, demanding much more time in individuals who smoke, than in those who do not smoke.

Step-by-step explanation:

a, b) For the group of smoking individuals, the average time it takes to fall asleep and the standard deviation of those times is:

$\bar X_F={\frac{1}{n} \sum_{i=1}^n x_i = 43.7$

$S_F=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2}=16.9278$

a, b) For the group of non-smoking individuals, the average time it takes to fall asleep and the standard deviation of those times is:

$\bar X_{NF}={\frac{1}{n} \sum_{i=1}^n x_i = 30.32$

$S_{NF}=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2}=7.12783$

c. In the attached file you can see the diagram of points for the times, in the smoking and non-smoking groups.

d. Apparently the practice of smoking reduces the ability to fall asleep, demanding much more time in individuals who smoke, than in those who do not smoke.

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