Question

Many people believe that the moon influences the actions of some individuals. A study of dementia patients in nursing homes recorded various types of disruptive behaviors every day for 12 weeks. Days were classified as moon days if they were in a three-day period centered at the day of the full moon. For each patient the average number of disruptive behaviors was computed for moon days and for all other days. The data for the 15 subjects whose behaviors were classified as aggressive are presented in the table below. The patients in this study are not a random sample of dementia patients. However, we examine their data in the hope that what we find is not unique to this particular group of individuals and applies to other patients who have similar characteristics.

Patient	Moon days	Other days	Difference	Patient	Moon days	Other days	Difference
1	3.34	0.27	3.07	9	6.01	1.59	4.42
2	3.66	0.59	3.07	10	4.34	0.60	3.74
3	2.67	0.32	2.35	11	3.34	0.65	2.69
4	3.33	0.19	3.14	12	0.68	0.69	-0.01
5	3.34	1.26	2.08	13	1.33	1.26	0.07
6	3.67	0.11	3.56	14	0.33	0.23	0.10
7	4.68	0.30	4.38	15	2.00	0.38	1.62
8	2.68	0.40	2.28

To analyze these paired data, we first subtract the disruptive behaviors for other days from the disruptive behaviors for moon days. These 15 differences form a single sample. They appear in the "Difference" columns in the table. The first patient, for example, averaged 3.34 aggressive behaviors on moon days but only 0.27 aggressive behaviors on other days. The difference

3.34 − 0.27 = 3.07

is what we will use in our analysis.

The results of the significance test allow us to conclude that dementia patients exhibit more aggressive behaviors in the days around a full moon. What are the implications of the study for the administrators who run the facilities where these patients live? For example, should they increase staff on these days? To make these kinds of decisions, an estimate of the magnitude of the problem, with a margin of error, would be helpful. (Round your answers to three decimal places.)

The 15 differences have sample mean

x = 2.437

and sample standard deviation

s = 1.462.

A 95% confidence interval for the mean difference in aggressive behaviors per day requires the critical value

t* =

from Table D. The margin of error is calculated below.

t*

s

n

=

=

Thus, the confidence interval is

x ± t*

s

n

=

±

=

, .

The estimated average difference is aggressive behaviors per day, with margin of error for 95% confidence. The increase needs to be interpreted in terms of the baseline values. The average number of aggressive behaviors per day on other days for our 15 patients is

;

on moon days it is

.

This is approximately a 400% increase. If aggressive behaviors require a substantial amount of attention by staff, then administrators should be aware of the increased level of these activities during the full-moon period. Additional staff may be needed.

Answer 1