In Exercises 11231128 use Procedure 111 on page 446 to nd th

In Exercises 11.23–11.28, use Procedure 11.1 on page 446 to nd the required condence interval. Be sure to check the conditions for using that procedure.

The Nipah Virus. From fall 1998 through mid 1999, Malaysia was the site of an encephalitis outbreak caused by the Nipah virus, a paramyxovirus that appears to spread from pigs to workers on pig farms. As reported by K. Goh et al. in the paper “Clinical Features of Nipah Virus Encephalitis among Pig Farmers in Malaysia” (New England Journal of Medicine, Vol. 342, No. 17, pp. 1229–1235), neurologists from the University of Malaysia found that, among 94 patients infected with the Nipah virus, 30 died from encephalitis.

a. Find a 90% condence interval for the percentage of Malaysians infected with the Nipah virus who will die from encephalitis.

b. Interpret your answer in part (a).

Solution

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.319148936          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.048079377          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.079083538          
lower bound = p^ - z(alpha/2) * sp =   0.240065398          
upper bound = p^ + z(alpha/2) * sp =    0.398232474          
              
Thus, the confidence interval is              
              
( 24.0065398% , 39.8232474% ) [ANSWER]

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b)

We are 90% confident that the true percentage of Malaysians infected with the Nipah virus who will die from encephalitis is between 24.007% and 39.823%. [ANSWER]