An epidemiologist with the Florida Department of Health needs to estimate the proportion of Floridians who are infected with the corona virus but are asymptomatic (show no signs of the virus). The epidemiologist compiled a preliminary random sample of infected patients and found that 65% of the sample were also asymptomatic. How large a sample should be selected such that the margin of error of the estimate for a 96% confidence interval is at most 1.93%. Round the solution up to the nearest whole number.

Afra is working in a bank. She has randomly contacted 36 customers and has examined their average annual salary. She found that the average salary of this sample of customers is $68200 with a sample standard deviation of $2375. She needs to report the population average at 95% confidence interval. What is the range that she should report?

A random sample of high school seniors were asked whether they were applying for college. The resulting confidence interval for the proportion of students applying for college is (0.65,0.69). What is the margin of error?

A company that manufactures baseball bats believes that its new bat will allow players to hit the ball 30 feet farther than its current model. The owner hires a professional baseball player known for hitting home runs to hit ten balls with each bat and he measures the distance each ball is hit to test the company's claim. The results of the batting experiment are shown in the following table. Construct a 90 % confidence interval for the true difference between the mean distance hit with the new model and the mean distance hit with the older model. Assume that the variances of the two populations are the same. Let Population 1 be the distances of balls hit with the new model baseball bat and Population 2 be the distances of balls hit with the old model. Round the endpoints of the interval to one decimal place, if necessary. Hitting Distance (in Feet) New Model 246 240 272 262 237 250 247 235 261 216 Old Model 293 232 299 279 239 228 256 292 272 298

An environmental health officer has been asked about levels of radon in homes in a particular county. As an initial step to forming a response to this inquiry, the officer plans to randomly select 20 homes in the county. The level of radon in each of the 20 homes will be measured, and the sample mean, x̅, and the sample standard deviation, s, will be calculated. Using these values, a 90% confidence interval will be constructed for the mean radon level for all homes in the county. Which of the following is the correct value of "t" for forming a confidence interval? a) 1.645 b) 1.328 c) 1.325 d) 1.725 e) 1.729

A company that manufactures baseball bats believes that its new bat will allow players to hit the ball 3030 feet farther than its current model. The owner hires a professional baseball player known for hitting home runs to hit ten balls with each bat and he measures the distance each ball is hit to test the company’s claim. The results of the batting experiment are shown in the following table. Construct a 90%90% confidence interval for the true difference between the mean distance hit with the new model and the mean distance hit with the older model. Assume that the variances of the two populations are the same. Let Population 1 be the distances of balls hit with the new model baseball bat and Population 2 be the distances of balls hit with the old model. Round the endpoints of the interval to one decimal place, if necessary.  Hitting Distance (in Feet) New Model Old Model 264264 271271 232232 264264 261261 275275 251251 258258 205205 249249 293293 235235 207207…

In a two-proportion study, we have p1= 0.682 with a sample size of 49 and p2= 0.612 with a sample size of 54. What would be the standard error in computing a confidence interval for the difference of proportions?

A telephone poll of 500 adult Americans was reported in an issue of Time Magazine.  One of the questions asked was “What is the main problem facing the country?”   Thirty percent answered “crime”.  We are interested in the population proportion of adult Americans who feel that crime is the main problem. Define the random variables X and P’ in words. Which distribution should be used for this problem? Explain your choice. Construct a 97% confidence interval for the population proportion of adult Americans who feel that crime is the main problem.      i.   State the confidence interval,   ii.  Sketch the graph,  iii. Calculate the error bound 4.  Suppose we want to lower the sampling error. What is one way to accomplish that?

A consumer agency estimate the proportion of all drivers who wear seat belts while driving. What is the most conservative estimate of the sample size that would limit the margin of error to within 0.06 of the population proportion for a 99 % confidence interval ?