A study was conducted to compare the efficacy of a mandibular advancement splint (MAS) and a tongue stabilizing device (TSD) in the treatment of obstructive sleep apnea (OSA). Thirty patients (20 male, 10 female) were recruited to the study with fifteen patients being randomly allocated to each treatment group. The efficacy of the treatments were compared using the apnea-hypopnea index (AHI).

Question 1

The thirty patients at the commencement of the study had an average AHI of 31.39 with a sample standard deviation of 12.34. After two months the AHI of each patient was again measured.

The MAS treatment group experienced an average reduction in AHI of 8.69 with a sample standard deviation of 9.30.

The TSD treatment group experienced an average reduction in AHI of 7.80 with a sample standard deviation of 10.65.

The standard error for the population mean AHI of patients at commencement is

0.411

1.577

2.253

5.731

Question 2

The margin of error for a 95% confidence interval of the population mean AHI of patients at commencement is

3.828

4.147

4.601

4.608

Question 3

Let M be the population mean decrease in AHI for the MAS treatment and let T be the population mean decrease in AHI for the TSD treatment. The researchers would like to test

H0:M=TvsH1:M

H0:M=TvsH1:MT

H0:M=0vsH1:M>0

H0:M=TvsH1:M>T

Question 4

The standard error for the difference in the sample means for the two treatment groups is

1.153

3.651

3.746

13.328

Question 5

The t statistic used to test the hypotheses in Question 3 is

0.188

0.244

0.321

0.772

Question 6

t test by hand, we can use the minimum degrees of freedom from the two samples. Here the degrees of freedom to be used is

14

23

28

29

Question 7

Based on the t test, using your degrees of freedom from Question 6, you can conclude that there is

no evidence to suggest that there is a difference in mean decrease in AHI between the two treatments (p > 0.1)

weak evidence to suggest that there is a difference in mean decrease in AHI between the two treatments (p < 0.1)

moderate evidence to suggest that there is a difference in mean decrease in AHI between the two treatments (p < 0.05)

strong evidence to suggest that there is a difference in mean decrease in AHI between the two treatments (p < 0.01)

Question 8

Assuming the original data was available, which of the following tests would provide a legitimate alternative to test the hypotheses of Question 3?

Signed-rank test

Rank-sum test

Chi-squared test

Sign test

Question 9

A secondary measure ("response to treatment") was defined as resolution of all symptoms or an improvement in symptoms and 50% reduction in AHI. In the MAS group 12 patients experienced a "response to treatment".

The standard error for the proportion of patients in the MAS group that experience a "response to treatment" is

0.0413

0.1033

0.1633

0.4575

Question 10

Constructing a 95% confidence interval by hand for the population proportion of patients in the MAS group that would experience a "response to treatment", the margin of error is

0.2024

0.2215

0.2403

0.7309

Question 11

In addition to the 12 patients in the MAS group who experienced a "response to treatment", 6 patients in the TSD group also experienced a "response to treatment". The standard error for the difference in the proportion of patients experiencing a "response to treatment" between the two groups is

0.0413

0.1033

0.1633

0.4575

Question 12

The researchers would like to test if there is a difference in the population proportion of patients that experience a "response to treatment" between the two treatment groups. Carrying out this test by hand, you can conclude there is

no evidence to suggest that there is a difference in the population proportion of patients that experience a "response to treatment" (p > 0.1)

weak evidence to suggest that there is a difference in the population proportion of patients that experience a "response to treatment" (p < 0.1)

moderate evidence to suggest that there is a difference in the population proportion of patients that experience a "response to treatment" (p < 0.05)

strong evidence to suggest that there is a difference in the population proportion of patients that experience a "response to treatment" (p < 0.01)