24 Postponing Death An interesting and popular hypothesis is

24.

Postponing Death An interesting and popular hypothesis is that individuals can temporarily postpone death to survive a major holiday or important event such as a birthday. In a study of this phenomenon, it was found that there were 6062 deaths in the week before Thanksgiving, and 5938 deaths the week after Thanksgiving (based on data from “Holidays, Birthdays, and Postponement of Cancer Death,” by Young and Hade, Journal of the American Medical Association, Vol. 292, No. 24). If people can postpone death until after Thanksgiving, then the proportion of deaths in the week before should be less than 0.5. Use a 0.05 significance level to test the claim that the proportion of deaths in the week before Thanksgiving is less than 0.5. Based on the result, does there appear to be any indication that people can temporarily postpone death to survive the Thanksgiving holiday?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.5
Ha:   p   <   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.505166667      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.004564355      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.131959952      
          
As this is a    left   tailed test, then, getting the p value,  
          
p = 0.871174364

  
significance level =    0.05      

Comparing p > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

There is no significant evidence that the proportion of deaths in the week before Thanksgiving is less than 0.5.

Based on the result, there appears to be no indication that people can temporarily postpone death to survive the Thanksgiving holiday.