t-score homework
HW: Set A1. A recent study of 28 employees of XYZ company showed that the mean of the distance they traveled to work was 14.3 miles. The standard deviation of the sample mean was 2 miles. Find the 95% confidence interval of the true mean. If a manager wanted to be sure that most of his employees would not be late, how much time would he suggest they allow for the commute if they average speed were 30 miles per hour?
2. A meteorologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 15 miles per hour. The standard deviation of the sample was 1.7 miles per hour. Find the 99% confidence interval of the true mean. If a meteorologist wanted to use the highest speed to predict the times it would take storms to travel across the state in order to issue warnings, what figure would she likely use?
3. The national average for the number of students per teacher for all U.S. public schools is 15.9. A random sample of 12 school districts from a moderately populated area showed that the mean number of students per teacher was 19.2 with a standard deviation of 2.1.Eastimate the true mean number of students per teacher with a 95% confidence. How does your estimate compare with the national average?
HW: Set B
1. The U.S. average for state and local taxes for a family of four is $4172. A random sample of 20 families in Maryland indicates they paid an annual amount of $4560 with a sample standard deviation of $1590. At α=0.05, is there sufficient evidence to conclude that they pay more than the national average of $4172?
2. A report by the Gallup Poll stated that on average a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women of the age of 18 years old, and obtained these data. At α=0.05, can it be concluded the average is still 5.8 visits/year? {3, 2, 1, 3, 7, 2, 9, 4, 6, 6, 8, 0, 5, 6, 4, 2, 1, 3, 4, 1}
3.A tire manufacturer is considering a newly designed tread pattern for its all-weather tires. Tests have indicated that these tires will provide better gas mileage and longer treat life. The last remaining test is for breaking effectiveness. The company hopes the tire will allow a car traveling at 60 mph will complete a stop within an average of 125 feet after the brakes are applied. They will adopt the new tread pattern unless there is strong evidence that the tires do not meet this objective. The distances, in feet, for 10 stops on a track test were 129, 128, 130, 132, 135, 123, 102, 125, 128, and 130. Should the company adopt the new tread pattern? How should the engineers deal with the outlier in the data?
HW: Set C
1. IN 1998, as an advertising campaign, the Nabisco Company announced a “1000 Chips Challenge,” claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chips. Dedicated Statistics students at the Air Force Academy (no kidding) purchase some randomly selected bags of cookies, and counted the chocolate chips. Here is some of their data: {1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135}. Test Nabisco's thousand chip claim.
2. The average number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Should the personnel team believe that the average number is about 10?