19 what sample size should a researcher take if he wants to

19) what sample size should a researcher take if he wants to estimate a population proportion to be withing 2% of the true value with 90% confidence?

20)What sample size should a researcher take if he wants to estimate a population proportion to be within 3% of the true value with 95% confidence? Previous research suggests the proportion is equal to 25%.

21) To estimate the proportion of teen traffic deaths in Texas last year that was caused by speeding, determine the necessary sample size for the estimate to be accurate to within .05 with probability .99.

a) suppose from a previous study, we expect the proportion to be about .30.

b) Suppose we do not have any prior knowledge about the true proportion.

Solution

19.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.64
Samle Proportion = 0.5
ME = 0.02
n = ( 1.64 / 0.02 )^2 * 0.5*0.5
= 1681 ~ 1681

20.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Samle Proportion = 0.25
ME = 0.03
n = ( 1.96 / 0.03 )^2 * 0.25*0.75
= 800.3333 ~ 801