A professor would like to use a 90% confidence interval to estimate the mean amount of time IRSC students spend studying each week. The professor knows that distribution of time spent studying each week by IRSC students is normally distributed with a standard deviation of 12.5 hours. How large a sample should the professor select to ensure the confidence interval has a width of no more than 5.38 hours. Round the solution up to the nearest whole number. n=

A researcher would like to estimate the mean weight of all adult male American alligators in the Everglades. The mean weight of a random sample of 49 adult male American alligators from the Everglades was found to be 541 pounds. The standard deviation of the weights of all adult male American alligators in the Everglades is known to be 20 pounds. Using a 96% confidence level, determine the margin of error, E, and a confidence interval for the mean weight of all adult male American alligators in the Everglades. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary. The margin of error is given by E= A 96% confidence interval is given by .

An economist would like to estimate the average household income in Okechobee county. The mean household income of a random sample of 150 families in Okechobee county was found to be $38,424. The standard deviation of the household incomes of all households in Okechobee county is known to be $939. Using a 99% confidence level, determine the margin of error, E, and a confidence interval for the average household income in Okechobee county. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary. The margin of error is given by E= A 99% confidence interval is given by

An agronomist would like to estimate the average weight of all Indian River County grapefruits. The mean weight of a random sample of 215 Indian River County grapefruits was found to be 210 grams. The standard deviation of the weights of all Indian River County grapefruit is known to be 12 grams. Find three different confidence intervals - one with a 99% confidence level, one with a 98% confidence level, and one with a 97% confidence level - for the mean weight of all Indian River County grapefruits. Notice how the confidence level affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Round solutions to two decimal places, if necessary.

• The margin of error for a 99% confidence interval is given by E=. A 99% confidence interval is given by .
• The margin of error for a 98% confidence interval is given by E=. A 98% confidence interval is given by .
• The margin of error for a 97% confidence interval is given by E=. A 97% confidence interval is given by .

If the level of confidence is decreased, leaving all other characteristics constant, the margin of error of the confidence interval will Select an answer increase decrease . If the level of confidence is decreased, leaving all other characteristics constant, the width of the confidence interval will Select an answer increase decrease .

The Florida Department of Transportation (FDOT) would like to estimate the average speed of vehicles on the Florida Turnpike. The mean speed, in miles per hour, of a random sample of vehicles was found to be 78 miles per hour. The standard deviation of the speeds of all vehicles on the Florida Turnpike is known to be 12 miles per hour. Find three different confidence intervals - one with sample size 128, one with sample size 234, and one with sample size 413. Assume that the mean of each sample is 78 miles per hour. Notice how the sample size affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Round solutions to two decimal places, if necessary.

• When n=128, the margin of error for a 97% confidence interval is given by . When n=128, a 97% confidence interval is given by .
• When n=234, the margin of error for a 97% confidence interval is given by . When n=234, a 97% confidence interval is given by .
• When n=413, the margin of error for a 97% confidence interval is given by . When n=413, a 97% confidence interval is given by .

If the sample size is increased, leaving all other characteristics constant, the margin of error of the confidence interval will Select an answer increase decrease . If the sample size is increased, leaving all other characteristics constant, the width of the confidence interval will Select an answer decrease increase .

Use the Student's t-distribution to find the t-value for each of the given scenarios. Round t-values to four decimal places.

• Find the value of t such that the area in the left tail of the t-distribution is 0.025, if the sample size is 33. t=
• Find the value of t such that the area in the right tail of the t-distribution is 0.1, if the sample size is 44. t=
• Find the value of t such that the area in the left tail of the t-distribution is 0.05, if the sample size is 51. t=
• Find the two values of t such that 98% of the area under the t-distribution is centered around the mean, if the sample size is 38. Enter the solutions using a comma-separated list. t= Use the Student's t-distribution to find the t-value for each of the given scenarios. Round t-values to four decimal places.
• Find the value of t such that the area in the right tail of the t-distribution is 0.05, if the sample size is 78. t=
• Find the value of t such that the area in the left tail of the t-distribution is 0.025, if the sample size is 129. t=
• Find the value of t such that the area in the left tail of the t-distribution is 0.005, if the sample size is 85. t=
• Find the two values of tt such that 99% of the area under the t-distribution is centered around the mean, if the sample size is 67. Enter the solutions using a comma-separated list. t=

A marine biologist would like to estimate the mean lifespan of all Florida manatees. The mean lifespan of a random sample of 34 Florida manatees was found to be 51 years. The standard deviation of the lifespans of all Florida Manatees is known to be 5.4 years. Using an 80% confidence level, determine a confidence interval for the mean lifespan of all Florida Manatees. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary. An 80% confidence interval is given by . Suppose the population standard deviation was unknown, but the marine biologist found the standard deviation of the lifespan of the sample of 34 Florida manatees was 7 years (along with the sample mean of 51 years). Determine a 80% confidence interval for the mean lifespan of all Florida manatees using this new information An 80% confidence interval is given by

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 45 trucks were tested for highway fuel economy and the sample had a mean of 27 miles per gallon with a standard deviation of 1.2 miles per gallon. Using a 98% 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 98% confidence interval is given by

A local non-profit group would like to estimate the proportion of residents of Martin county who do not have health insurance. To help with this estimate, the non-profit surveyed a random sample of Martin county residents and found that 10% did not have heath insurance. Determine the sample size required to limit the margin of error to within 0.077 of the population proportion for a 98% confidence interval. Round the solution up to the nearest whole number. n=

An economist needs to estimate the proportion of residents of Vero Beach that have earned a college degree. Determine the most conservative estimate of the sample size required to limit the margin of error to within 0.086 of the population proportion for a 90% confidence interval. Round the solution up to the nearest whole number. n=

A campaign staffer would like to estimate the proportion of likely voters who will vote for a particular candidate in the upcoming election. To help with this estimate, the staffer surveyed a small group of likely voters and found that 71% of the sample supported the candidate. How large a sample should be selected such that the margin of error of the estimate for a 99% confidence interval is at most 3.8%. Round the solution up to the nearest whole number. n=

Americans are stressed out! A psychologist would like to estimate the proportion of Americans that say "the future of the nation is a significant source of stress for me." To help form an estimate, the psychologist randomly selected 650 Americans and found that 63% of the sample agreed with the statement "the future of the nation is a significant source of stress for me." Using a 95% confidence level, determine the margin of error, E, and a confidence interval for the true proportion of all Americans that say the "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 95% confidence interval is given by