Researchers are interested in estimating the prevalence of hypertension in a pop

Question

Researchers are interested in estimating the prevalence of hypertension in a population of adults aged 40-65 for a new grant. Suppose the population prevalence is 37.5%. The research team has enrolled 167 participants, and 79 have been confirmed hypertensive.

A)   Can we approximate with the normal distribution in this hypothetical example? Why or why not?

B)   Create a standardized z-score for the estimate calculated by the research team.

C) What is the probability of observing at least 79 to be confirmed hypertensive from this sample?

Explanation / Answer

a) Yes we can  approximate with the normal distribution in this hypothetical example as here n=167 and p=0.375

hence np and n(1-p) both are greater then 10. hence condition fulfilled.

b)

here mean =np=167*0.375=62.625

and std deviaiton =(np(1-p))1/2=6.256

hence standarized z score  for the estimate calculated by the research team =Z(X=79)=(X-mean)/std deviation

=(79-62.625)/6.256=2.6174

c) P(X>=79)=1-P(X<=78)=1-P(Z<(78.5-62.625)/6.256)=1-P(Z<2.5375)=1-0.9944=0.0056

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