6.5 Vasoconstrictor responses to the intra-arterial injection of epinephrine wer
ID: 3306965 • Letter: 6
Question
6.5 Vasoconstrictor responses to the intra-arterial injection of epinephrine were ob- tained in the perfused hindpaws of dogs. Responses were obtained before and 30 minutes after the intramuscular (i.m.) administration of cocaine hydrochloride, 5 mg/kg im. Vasoconstriction was indicated by the increases in perfusion pressure. 210 COMPARISON OF TWO GROUPS:t-TESTS AND RANK TESTS Perfusion Pressure (mm Hg Number Precocaine Postcocaine 78 36 24 28 64 24 24 110 64 20 Use a nonparametric test to test the hypothesis of equal response distributions pre-and postcocaine administration. Use -0.05 (a) (b) What is the signed-rank estimate of d? (c) Place a 90% confidence interval on d.Explanation / Answer
(a) We use a sign test as the samples are paired.
We calculate the deviation as follows:
The null hypothesis in this case is H0: P(X-Y>0)=1/2 and P(X-Y<0)=1/2
The random variable Ui is defined as UI=1 if X-Y>0 and UI=1 if X-Y<0
We consider another random variable U, which is considered as a binomial variate with p=1/2 as defined in the null hypothesis and n=7 since we ignore the tie value of 0. The random variableU is defined as U= Ui
For our given data U=3, Thus P(U3) = P(U=0) + P(U=1) +P(U=2) +P(U=3)
P(U3) = 0.0078125 + 0.0546875 + 0.1640625 + 0.2734375
P(U3) = 0.5
The level of significance is 0.05. Here, it is observed that the p-value is grater than the significant value. Hence we accept our null hypothesis H0.
(b) The sign rank estimate of µd is given by np = 7x0.7 = 3.5
(c) the variance of µd is npq = 7x 0.5 x 0.5 = 1.75
and the critical values of a 90% two sided confidence interval is ±1.645
Thus, the 90% confidence interval is given by 3.5 ±1.645x1.75 =3.5 ± 2.87875 = (0.62125, 6.3787)
DOG Prococaine(X) Postcocaine(Y) X-Y Sign Ui 1 40 78 -38 - 0 2 24 36 -12 + 1 3 6 6 0 - - 4 28 24 4 + 1 5 64 110 -46 - 0 6 24 64 -40 - 0 7 8 20 -12 - 0 8 44 40 4 + 1Related Questions
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