Show ALL STEPS OR THE ANSWERS ARE USELESS. Use the standard normal distribution

Question

Show ALL STEPS OR THE ANSWERS ARE USELESS. Use the standard normal distribution table, the t distribution table the chi-square distribution table or the f distribution table IF needed and when needed.

ESTION 2 (4 marks in total) A medical experiment is being conducted to determine the recovery rate of patients given a new drug. In particular, the researcher would like to estimate the proportion of patients who fully recover within one week from when they begin taking the drug. How large should the sample size be so that a 98% confidence interval for the population proportion has a margin of error of 0.04? Assume that a preliminary sample suggests the proportion is 0.80.

Explanation / Answer

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.01  
       
      
Using a table/technology,      
      
z(alpha/2) =    2.33  
      
Also,      
      
E =    0.04  
p =    0.8  
      
Thus,      
      
n =    542.89  
      
Rounding up,      
      
n =    543   [ANSWER]

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