Question

A study involves 634 randomly selected deaths, with 29 of them caused by accidents. a.Construct a 99% confidence interval for the percentage of all deaths that are caused by accidents.b.Write a summary statement for the 99% confidence interval.

Answer 1

Here we have given that,

n= number of persons selected deaths=634

x: number of persons caused death by accidencts = 29

Now, we estimate the proportion p as

=sample proportion =

Now we want to find the 99% confidence interval for population proportion P

Formula for CI is as follows,

Now we find Zcritical

c=confidence level=0.99

=level of significance=1-c=1-0.99= 0.01

Zcritical = 2.58

99% confidence interval is

0.046 - 0.016 \leq P \leq 0.046 + 0.016

0.030 \leq P \leq 0.062

Conclusion:

Here we can say that we are 99 % confident that the population proportion is lies within that interval.