The number of births per hour during a given day was recorded for a certain metr

Question

The number of births per hour during a given day was recorded for a certain metropolitan hospital. The probability that a baby will be born in that hospital is 0.08. In such situations we are often interested in whether the events occur randomly in time or space. (a) Test the hypothesis that the number of babies born per hour was randomly at alpha = 0.05, (b) Give the Null and Alternative Hypotheses. (c) Draw a curve showing the Critical Value(s) and make a Statistical Decision. (d) Write a one-sentence conclusion. Data follows:

Explanation / Answer

Solution:

Test hypothesis

Ho: Number of babies born per hour is random
H1: Number of babies born per hour is not random

As under Ho the number of born babies is random so no. of born babies are uniformly distributed

For uniform distirbution we have mean = a+b/2
= 0+4/2 = 2

Test statistics under Ho is

Cal t = (x-)*sqrt(n)/s
= (2 - 1.8)*sqrt(24)/1.24
= 0.2 * 4.89897/1.24
= 0.7901

Tab t23, 0.025 as alternative is two sided

tab t23,0.025 = 2.069

as cal t < tab t we fail to reject null hypothesis and conclude that number of babies born are randomly distributed

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