Question

In: Statistics and Probability

An investigator wants to estimate the proportion of freshman at his university who currently smoke cigarettes....

An investigator wants to estimate the proportion of freshman at his university who currently smoke cigarettes. How many freshman should be involved in the study to ensure that a 90% confidence interval estimate of the proportion is within 0.04 of the true proportion?

Solutions

Expert Solution

Solution :

Given that,

= 0.5

1 - = 0.5.

margin of error = E = 0.04

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.645 / 0.04)2 * 0.5 * 0.5

=422.816

Sample size = 423


Related Solutions

1. A university wants to estimate the proportion of its students who smoke regularly. Suppose that...
1. A university wants to estimate the proportion of its students who smoke regularly. Suppose that this university has N = 30, 000 students in total and a SRSWOR of size n will be taken from the population. a) If the university wants the proportion estimator ˆp to achieve the precision with tolerance level e = 0.03 and risk α = 0.1. Estimate the minimal sample size needed for this estimation. (z0.1 = 1.28, z0.05 = 1.65) b) Suppose that,...
Suppose the prime minister wants an estimate of the proportion of the population who support his...
Suppose the prime minister wants an estimate of the proportion of the population who support his current policy on health care. The prime minister wants the estimate to be within 0.21 of the true proportion. Assume a 90% level of confidence. The prime minister's political advisors estimated the proportion supporting the current policy to be 0.48. (Round the intermediate calculation to 2 decimal places. Round the final answer to the nearest whole number.) a. How large of a sample is...
Suppose the U.S. president wants an estimate of the proportion of the population who support his...
Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within 0.03 of the true proportion. Assume a 98% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.54. a.) How large of a sample is required? (Round the z-values to 2 decimal places. Round up your answer to the next...
Suppose the U.S. president wants an estimate of the proportion of the population who support his...
Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within 0.03 of the true proportion. Assume a 98% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.54. a.) How large of a sample is required? (Round the z-values to 2 decimal places. Round up your answer to the next...
Suppose the prime minister wants an estimate of the proportion of the population who support his...
Suppose the prime minister wants an estimate of the proportion of the population who support his current policy on health care. The prime minister wants the estimate to be within 0.21 of the true proportion. Assume a 90% level of confidence. The prime minister's political advisors estimated the proportion supporting the current policy to be 0.48. (Round the intermediate calculation to 2 decimal places. Round the final answer to the nearest whole number.) a. How large of a sample is...
Suppose the U.S. president wants an estimate of the proportion of the population who support his...
Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within 0.02 of the true proportion. Assume a 95% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.59. (Use z Distribution Table.) a. How large of a sample is required? (Round the z-values to 2 decimal places. Round up your...
Suppose the prime minister wants an estimate of the proportion of the population who support his...
Suppose the prime minister wants an estimate of the proportion of the population who support his current policy on health care. The prime minister wants the estimate to be within 0.03 of the true proportion. Assume a 80% level of confidence. The prime minister's political advisors estimated the proportion supporting the current policy to be 0.3. (Round the intermediate calculation to 2 decimal places. Round the final answer to the nearest whole number.) a. How large of a sample is...
Suppose the U.S. president wants an estimate of the proportion of the population who support his...
Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within 0.03 of the true proportion. Assume a 90% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.56. (Use z Distribution Table.) a. How large of a sample is required? (Round the z-values to 2 decimal places. Round up your...
1. We are interested in estimating the proportion of students at a university who smoke. Out...
1. We are interested in estimating the proportion of students at a university who smoke. Out of a random sample of 200 students from this university, 40 students smoke. (1) Calculate a 95% confidence interval for the proportion of students at this university who smoke and interpret this interval in context. (2) If we wanted the margin of error to be no larger than 2% at a 95% confidence level for the proportion of students who smoke, how big of...
A town council wants to estimate the proportion of residents who are in favor of a...
A town council wants to estimate the proportion of residents who are in favor of a proposal to upgrade the computers in the town library. A random sample of 100 residents was selected, and 97 of those selected indicated that they were in favor of the proposal. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT