Researchers are interested in estimating the prevalence of obesity in a populati

Question

Researchers are interested in estimating the prevalence of obesity in a population of adults aged 40-65 for a new grant. Suppose the population prevalence is 35%. The research team has enrolled 275 participants,

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

What is the expected number of obese participants in this sample? State also its variance.

C. What is the probability of observing at least 130 to be confirmed obese from this sample?

D. Out of the 275 participants in the study, 130 were confirmed to be obese. Based on your answer to part C, do you then believe that the 35% value for prevalence is accurate? Justify your answer with statistical reasoning.

Explanation / Answer

Yes, we can approximate with the normal distribution in this hypothetical example

expected number of obese participants in this sample = 0.35*275 = 96.25

Variance = 0.35*0.65*275 = 62.5625

P(X>=130)

Use Excel function

1-NORMSDIST(129,275,0.35,TRUE)

= 0.000019

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