Instructions An interesting and popular hypothesis is that i

Instructions:

An interesting and popular hypothesis is that individuals can postpone their death to survive a major holiday or imporant event such as a birthday. In a study of this phenomenon, it was found that in the week before and the week after Thanksgiving, there were 12,000 total deaths, and 6062 of them occured in the week before Thanksgiving (based on the data from Holidays, Birthdays and Postponement of Cancer Death,\" by Young and Hade, Journal of the Ameruican Medical Association, Vol. 292, No. 24.

a. What is the best point estimate of the proportion of deaths in the week before Thanksgiving to the the total deaths in the week before and the week after Thanksgiving?

b. Construct a 95% confidence interval estimate of the proportion of deaths in the week before Thanksgiving to the total deaths in the week before and the week after Thanksgiving.

c. Based on the result, does there appear to be any indication that people can temporararily postpone their death to survive the Thanksgiving holiday? Why or why not?

Solution

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.505166667   [ANSWER]

******************

b)      
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.004564111          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.008945493          
lower bound = p^ - z(alpha/2) * sp =   0.496221174          
upper bound = p^ + z(alpha/2) * sp =    0.51411216          
              
Thus, the confidence interval is              
              
(   0.496221174   ,   0.51411216   ) [ANSWER]

***********************

c)

No, because 0.50 is still inside the confidence interval. [ANSWER]