Question

Doctors use several kinds of medications to treat the symptoms and complications of COPD; some are taken on a regular basis and others as needed:

• Bronchodilators. These medications — which usually come in an inhaler — relax the muscles around your airways. Inhaled steroids. Inhaled corticosteroid medications can reduce airway inflammation and help prevent exacerbations. Combination inhalers. Some medications combine bronchodilators and inhaled steroids. Salmeterol and fluticasone (Advair) and formoterol and budesonide (Symbicort) are examples of combination inhalers. So our focus for this question is the Advair Diskus and Symbicort; both maintenance inhalers and often compared. Advair Diskus may begin working within 30 – 60 minutes and Symbicort may begin working within 15 minutes, although results may vary in both cases. We visited the Bowmanville emergency department and monitored some of the recently admitted COPD patients who were placed on either Advair or Symbicort. One-hour after their medication was delivered, their SpO2 (peripheral capillary oxygen saturation) levels were recorded; the results were as follows: The raw and sorted data (smallest to largest) are shown below. SpO2 (%) (Raw data) SpO2 (%) (Sorted Raw Data) Advair Symbicort Advair Combined Symbicort Combined Rank Rank 90 93 88 90 88 90 89 90 90 97 90 93 89 90 90 93 90 93 90 96 96 97 97 97 Medians 90 93 Since it was not decided (hypothesized) which drug would offer the most benefit after one hour, use the Mann-Whitney U-Test to test the claim at 95% confidence that there is a difference in these two products. (Assume the median SpO2 results from the two drugs are significantly different from each other.) State the Null and Alternative Hypothesis (1) State the Decision Rule. (1) Determine U and U’ (4,4) Determine the Test statistic, Utest (1) State your Decision (1)

Answer 1

1). hypothesis:-

the two populations are equal.

the two populations are not equal. , =0.05

2).two sample sizes are:-

5 and 7

The critical value for this test with n₁=5, n₂=7 and α =0.05 is 5 .( from critical value table of U test)

so, the decision rule is : Reject H₀ if U < 5.

3).

advair	combined rank	Symbicort	combined rank
88	1	90	5
89	2	90	5
90	5	93	8.5
90	5	93	8.5
90	5	96	10
		97	11.5
		97	11.5
rank sum()	18	rank sum()	60

i.e U=32

i.e, U^*= 3

4).so our test statistic be:-

5).decision:-

since 3 <  5,

we reject the null hypothesis.

hence we conclude at 0.05 % level of significance ,

there is enough evidence to support the claim that there is a difference in these two products

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