Answered: A sleep disorder specialist wants to… | bartleby

MATLAB: An Introduction with Applications

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A sleep disorder specialist wants to test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night. To do so, the specialist randomly selects 16 patients and records the number of hours of sleep each gets with and without the new drug. The accompanying table shows the results of the two-night study. Construct a 90% confidence interval for \( \mu_d \), using the inequality:

\[
\bar{d} - t_c \frac{s_d}{\sqrt{n}} < \mu_d < \bar{d} + t_c \frac{s_d}{\sqrt{n}}
\]

Assume the populations are normally distributed.

[Insert clickable icon to view data on hours of sleep with and without the drug]

Calculate \( d \) for each patient by subtracting the number of hours of sleep with the drug from the number without the drug. The confidence interval is:

\[
[\text{lower bound}] \, \text{hr} < \mu_d < [\text{upper bound}] \, \text{hr}
\]

(Round to two decimal places as needed.)

# Hours of Sleep

This table illustrates the hours of sleep recorded for 16 patients, both without and with the use of a specific drug. The data is organized into two rows corresponding to sleep duration measurements:

- **Patient Numbers:** 1 through 16.
- **Hours of Sleep (without the drug):**
- Patient 1: 3.3 hours
- Patient 2: 1.9 hours
- Patient 3: 1.8 hours
- Patient 4: 2.3 hours
- Patient 5: 1.9 hours
- Patient 6: 3.4 hours
- Patient 7: 4.1 hours
- Patient 8: 2.7 hours
- Patient 9: 4.6 hours
- Patient 10: 4.4 hours
- Patient 11: 5.8 hours
- Patient 12: 4.4 hours
- Patient 13: 2.2 hours
- Patient 14: 3.1 hours
- Patient 15: 5.3 hours
- Patient 16: 5.7 hours

- **Hours of Sleep (using the drug):**
- Patient 1: 5.4 hours
- Patient 2: 4.3 hours
- Patient 3: 3.9 hours
- Patient 4: 3.8 hours
- Patient 5: 3.1 hours
- Patient 6: 4.5 hours
- Patient 7: 4.8 hours
- Patient 8: 5.0 hours
- Patient 9: 5.2 hours
- Patient 10: 6.1 hours
- Patient 11: 7.9 hours
- Patient 12: 5.5 hours
- Patient 13: 3.7 hours
- Patient 14: 5.5 hours
- Patient 15: 7.8 hours
- Patient 16: 6.6 hours

This data examines the effect of the drug on the sleep duration of each patient, highlighting potential increases in sleep time with the drug's use.

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