According to the World Health Organization, approximately 2/3 of the population

Question

According to the World Health Organization, approximately 2/3 of the population of humans under 50 years old, worldwide, are infected with the herpes simplex virus type I 2. (a) A doctor surveys a random sample of 5 humans (all younger than 50 years old) from around the world. What is the probability that none of the 5 people in his sample are infected with the herpes simplex virus type 1? (2 points) (b) The doctor then surveys a random sample of 5 UCSB students (all younger than 50 years old). The doctor finds that 1 student is infected with the herpes simplex virus type1 Based on his sample, is the proportion of herpes-infected UCSB students significantly less than the proportion of herpes-infected individuals worldwide? Perform the appropriate statistical test to arrive at your conclusion, and show your work. (3 points)

Explanation / Answer

(a)answer=0.0041

here we use binomial distribution with parameter n=5 and p=2/3 and for

Binomial distribution ,P(X=r)=nCrpr(1-p)n-r  

P(none of 5 people infected)= P(X=0)=0.0041 ( using ms-excel BINOMDIST(0,5,2/3,0) )

so required probability=0.0041

(b) here we want to test the

null hypothesis H0:P=2/3 and

alternate hypothesis H1:P<2/3

p=x/n=1/5

the test statistic z=(p-P)/SE(p)=(1/5 - 2/3)/sqrt((2/3)*(1-2/3)/5)=-2.214

the typical one tailed critical z(0.05)=1.645 is less than absolute value of the calculated z=2.214, so we fail to accept H0 ( or reject H0) and conclude that proportion of herpes infected UCSB sudents is significnatly less than proportion of herpes infected indiviual worldwide.

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