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 only 60 of 747 people whose obituaries were

published in Salt Lake City in 1975 died in the three-month period preceding their birthday.

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

preceding their birthday. Please clearly state your critical value.

2. Write a sentence explaining what the “90%” part of the confidence interval from the previous problem means.

3. How large of a sample would we need, at a 90% confidence level, to estimate the true proportion of people

who died in the three-month period preceding their birthday with a margin of error no greater than 0.001?

4. 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 Problem

1, and at a 5% significance level (i.e.α= 0.05), do we have convincing evidence that the true proportion of

deaths that occur in the three month period before a decedents’s birthday is less than 25%? Why?

Answer 1

1:

2:

We can be 90% confident that true proportion of people who die in the three-month period preceding their birthday lies in the interval (0.064, 0.097).

3:

4:

Since 0.25 is greater than lower limit, equal to 0.064, of 90% confidence interval so on the basis of confidence interval we cannot conclude that the true proportion of deaths that occur in the three month period before a decedents’s birthday is less than 25% at a 5% significance level.