Question

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.31

(b) there is no preliminary estimate for p

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of medical files is used to estimate the proportion p of all people who have blood type B.

If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.06 from p? (Round your answer up to the nearest whole number.)

____________medical files

Answer part (a) if you use the preliminary estimate that about 12 out of 90 people have blood type B.

_____________medical files

Answer 1

Solution:

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.31

Answer: The formula for finding the sample size is:

Where:

is the critical value at the 0.05 significance level.

(b) there is no preliminary estimate for p

Answer: Since there is no preliminary estimate for p, we, therefore, consider the estimate for p as 0.5

Where:

is the critical value at the 0.05 significance level.

A random sample of medical files is used to estimate the proportion p of all people who have blood type B.

If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.06 from p? (Round your answer up to the nearest whole number.)

144 medical files

Answer:

Where:

is the critical value at the 0.15 significance level.

Answer part (a) if you use the preliminary estimate that about 12 out of 90 people have blood type B.

67 medical files

Answer:

Where:

is the critical value at the 0.15 significance level.