SOLUTION: An epidemiologist is worried about the ever increasing trend of malaria in a certain locality and wants to estimate the proportion of people infected in the peak malaria transmiss

Question 1184274: An epidemiologist is worried about the ever increasing trend of malaria in a certain locality
and wants to estimate the proportion of people infected in the peak malaria transmission
period. If he takes a random sample of 150 people in that locality during the peak
transmission period and finds that 60 of them are positive for malaria, find
i. 99% confidence interval for the proportion of the whole infected people in that
locality during the peak malaria transmission period.
ii. Based on your results in part (i), do you think the epidemiologist’s worry is
justified? Explain.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample size is 150
60 are positive for malaria.
the mean proportion is 60/150 = 6/15 = 2/5 = .4
the mean proportion standard deviation is sqrt(.4 * .6) / 150) = .04
critical z-score for 99% two-tailed confidence level is plus or minus 2.5758.

the z-score formula is z = (x - m) / s
z is the z-score.
x is the sample raw score proportion.
m is the population mean proportion.
s is the standard error = sqrt(p*q/n), where:
p is the population proportion.
q = 1 - p
n is the sample size.

when z = -2.5758, the formula becomes:
-2.5758 = (x - .4) / .04
solve for x to get:
x = -2.5758 * .04 + .4 = .297

when z = 2.5758, the formula becomes:
2.5758 = (x - .4) / .04
solve for x to get:
x = 2.5758 * .04 + .4 = .503.

i believe that's your two-tailed confidence interval.

with a sample size of 150, between 30% and 505 will show positive for malaria.

that a very high percentage, showing that the population is at high risk for malaria.

here's a world malaria report that shows where the highest risks are.

https://www.gs.international/learning-centre-articles/malaria-world-map-risk

here's a reference on mean proportion and standard deviation.

https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Shafer_and_Zhang)/06%3A_Sampling_Distributions/6.03%3A_The_Sample_Proportion#:~:text=at%20least%2030.-,The%20Sampling%20Distribution%20of%20the%20Sample%20Proportion,interval%20%5B0%2C1%5D.

i'm never 100% certain that i'm right with these types of problems, but i'm reasonably certain that what i gave you is accurate.

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