There is a theory that people
There is a theory that people may tend to “postpone” theirdeaths until after some event that has
particular meaning to them has passed. Birthdays, a familyreunion, or the return of a loved one have
all been suggested as the sorts of personal milestones thatmight have such an effect. In a study to set
up to examine that notion statistically, it was found that only60 of 747 people whose obituaries were
published in Salt Lake City in 1975 died in the three-monthperiod preceding their birthday.
1. Construct a 90% confidence interval for the true proportionof people who die in the three-month period
preceding their birthday. Please clearly state your criticalvalue.
2. Write a sentence explaining what the “90%” part of theconfidence interval from the previous problem means.
3. How large of a sample would we need, at a 90% confidencelevel, to estimate the true proportion of people
who died in the three-month period preceding their birthday witha margin of error no greater than 0.001?
4. If individuals are dying randomly with respect to theirbirthday, we would expect 25% to die during the
three-month period preceding their birthday. Based on theconfidence interval you constructed in Problem
1, and at a 5% significance level (i.e.α= 0.05), do we haveconvincing evidence that the true proportion of
deaths that occur in the three month period before a decedents’sbirthday is less than 25%? Why?
Answer:
1:
2:
We can be 90% confident that true proportion of people who diein the three-month period preceding their birthday lies in theinterval (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 wecannot conclude that the true proportion of deaths that occur inthe three month period before a decedents’s birthday is less than25% at a 5% significance level.
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