There is a theory that people may tend to \"postpone\" their deaths until after

Question

There is a theory that people may tend to "postpone" their deaths until after some event that has particular meaning to them has passed. Birthdays, a family reunion, or the return of a loved one have all been suggested as the sorts of personal milestones that might have such an effect. In a study to set up to examine that notion statistically, it was found that 60 of 747 people whose obituaries were published in Salt Lake City in 1975 died in the three month period preceding their birthday.

2a. Construct a 90% confidence interval for the true proportion of people who die in the three-month period preceding their birthday.

2b. If Individuals are dying randomly with respect to their birthday, we would expect 25% to die during the three-month period preceding their birthday. Based on the confidence interval you constructed in part a, and at the 5% significance level, do we have convincing evidence that the true proportion of deaths that occur in the three month period before a decedent's birthday in less than 25%? Why

Explanation / Answer

a) here sample proportion phat =60/747=0.0803

for n=747 ; standard error =(phat(1-phat)/n)1/2 =0.0099

and for 90% confidence interval critical value of z =1.645

therefore 90% confidence interval for the true proportion =phat -/+ z*standard error =0.0640 ; 0.0967

2bb) as our confidence interval does not contain 25% (0.25) as an interval value we have have convincing evidence that the true proportion of deaths that occur in the three month period before a decedent's birthday in less than 25%.

please revert for any clarification required

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