An automobile manufacturer needs to estimate the average highway fuel economy (miles per gallon) for a new truck that will be sold starting next year. A random sample of 37 trucks were tested for highway fuel economy and the sample had a mean of 31.9 miles per gallon with a standard deviation of 1.4 miles per gallon.

Using a 90% confidence level, determine the margin of error, E, and a confidence interval for the average highway fuel economy of this new truck. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.

The margin of error is given by E =

A 90% confidence interval is given by =----

2- A psychologist would like to estimate the proportion of American that say "the future of the nation is a significant source of stress for me." To help form an estimate, the psychologist randomly selected 561 Americans and found that 61.8% of the sample agreed with the statement "the future of the nation is a significant source of stress for me."

Using a 98% confidence level, determine the margin error, E, and a confidence interval for the true proportion of all Americans that say the "future of the nation is a significant source of stress for me." Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary.

The margin of error is given by E =

A 98% confidence interval is given by ====

3= A college would like to estimate the proportion of its students that work full-time while going to school. A researcher at the college found that 304 students out of a random sample of 739 students worked full-time while going to school.

Determine the point estimate, p^ and the sample standard deviation, sp^. Round the sample proportion to four decimal places and round the standard deviation to six decimal places, if necessary.

p^ =

sp^ =

Using a 96% confidence level, determine the margin of error, E, and a confidence interval for the proportion of all students at the college who work full-time while going to school. Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary.

The margin of error is given by E =

A 96% confidence interval is given by =

4- The St Lucie County Health Department needs to estimate the proportion of county residents with diabetes. A health department researcher found that 115 out of a random sample of 1108 county residents had diabetes.

Determine the point estimate, p^ and the sample standard deviation, sp^. Round the sample proportion to four decimal places and round the standard deviation to six decimal places, if necessary.

p^ =

sp^ =

Using a 99% confidence level, determine the margin of error, E, and a confidence interval for the true proportion af all St. Lucie County residents who have diabetes. Report the confidence interval using interval notation. Round to four decimal places, if necessary.

The margin of error is given by E =

A 99% confidence interval is given by =.

5- An economist at Florida Department of Labor and Employment needs to estimate the unemployment rate in Okechobee county. The economist found that 3.6% of a random sample of 377 county residents were unemployed.

Find three different confidence intervals for the true proportion of Okechobee county residents who are unemployed. Calculate one confidence interval with a 90% confidence level, one with 95% confidence level, and one with a 99% confidence level. Notice how the confidence level affects the margin of error and the width of the interval.

Report confidence interval solutions using interval notation. Express solutions in percent form, rounded to two decimal places, if necessary

- The margin error for a 90% confidence interval is given by E =

A 90% confidence interval is given by ----

- The margin of error for a 95% confidence interval is given by E =

A 95% confidence interval is given by====

- The margin of error for a 99% confidence interval is given by E =

A 99% confidence interval is given by--====