Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years. a. Calculate a 95% two-sided confidence interval on the death rate from lung cancer.
b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03?
c. How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.03, regardless of the true value of p?

a)

The 95% confidence interval would be given by (0.799;0.847)

b)  

And rounded up we have that n=622

c)  

And rounded up we have that n=1068

Step-by-step explanation:

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and . And the critical value would be given by:

The confidence interval for the mean is given by the following formula:  

If we replace the values obtained we got:

The 95% confidence interval would be given by (0.799;0.847)

Part b

The margin of error for the proportion interval is given by this formula:  

   (a)  

And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

  (b)  

And replacing into equation (b) the values from part a we got:

And rounded up we have that n=622

Part c

And rounded up we have that n=1068

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent

i dont get the question

step-by-step explanation: