Question

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(Partially need MATLAB) Hockema et al. studied the craniofacial morphology of 26 male patients with obstructive sleep apnea syndrome (OSAS) and 37 healthy male subjects (non-OSAS). One of the variables of interest was the length from the most superoanterior point of the body of the hyoid bone to the Frankfort horizontal (measured in millimeters) Length (mm) Non-OSAS Length (mm) OSAS 96.80 97.00 101.00 88.95 105.95 114.90 113.70 114.90 114.35 116.30 110.35 2.25 108.75 123.10 06.15 13.30 119.30 02.60 106.00 110.00 102.40 101.75 98.95 105.05 114.20 2.65 108.95 28.95 105.05 7.70 00.70 97.70 88.25 101.05 94. 55 97.00 92.60 92.60 99.65 94.55 98.25 97.00 109.15 106.45 90.85 91.95 94.55 95.25 88.95 95.75 102.75 7.70 94.05 92.10 91.90 88.80 89.45 0.40 90.55 89.50 98.20 109.80 89.85 You can find the data in HW6 Data.xlsx (1) Please test the null hypothesis that the variances between two groups are equal (2) Based on the result from (1), do these data provide sufficient evidence to allow us to conclude that the two sampled populations differ with respect to length from the hyoid bone to the Frankfort horizontal Note: The result from question (1) is related to the assumption on population variances, i.e., equal or not. ii Please stl write Steps (1)-(6) in the testing procedure and clearly indicate whether the null hypothesis is rejeeted or not based on the MATLAB result for each problem.

Answer 1

NON-OSAS		OSAS
Mean	117.9891892	Mean	111.0596
Standard Error	22.04418348	Standard Error	1.364348
Median	95.75	Median	111.3
Mode	94.55	Mode	114.9
Standard Deviation	134.0895333	Standard Deviation	6.956839
Sample Variance	17980.00294	Sample Variance	48.3976
Kurtosis	36.86250476	Kurtosis	0.422001
Skewness	6.066303665	Skewness	0.51572
Range	822.65	Range	30
Minimum	88.25	Minimum	98.95
Maximum	910.9	Maximum	128.95
Sum	4365.6	Sum	2887.55
Count	37	Count	26

The provided sample varai 17980.00294 and 2 48.39760385 and the sample sizes are given by n137 and n2 26 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested This corresponds to a two-tailed test, for which a F-test for two population variances needs to be Based on the information provided, the significance level is a0.05, and the the rejection region for this two-tailed test is R-F:F< 0.491 or F>2.14 (3) Test Statistics The F-statistic is computed as follows: s 17980.00294 s3 48.39760385 371.506

(4) Decision about the null hypothesis Since from the sample information we get that F 371.506>Fu -2.14, it is then concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population variance σ| is different than the population variance σ , at the α 0.05 significance level Confidence Interval The 95% confidence interval for-L is. 173.624 756.766