Thread: confidence

Use the given degree of confidence and sample data to find the margin of error in estimating the population mean μ for the following scenario. College students' annual earnings: 99% confidence; n = 67, = $6068, s = $1000.




9.Find the margin of error for a sample of 12, where the mean is 61.4 and the standard deviation is 6.9. Use a 95% confidence interval.




10.The amounts (in ounces) of juice in eight randomly selected juice bottles are:

15.8 15.9 15.9 15.6 15.2 15.7 15.8 15.6

Construct a 98 percent confidence interval for the mean amount of juice in all such bottles.




11.The weekly earnings of students in one age group are normally distributed with a standard deviation of 100 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 5 dollars.

12.Smokey wishes to estimate the true proportion of all drivers who exceed the speed limit on a certain stretch of road where accidents frequently happen. How large should the sample be so that, with 93 percent confidence, the sample proportion will not differ from the true proportion by more than 0.01?




13.An estimate of the population proportion from a study on the incidence of hepatitis A in a certain time period is 0.25. In a new study, the researchers want a margin of error of 0.005 with 99% confidence level. Find the minimum sample size you should use to assure that your estimate, , will be within the required margin of error around the population p.




14.The owner of the Arizona Cardinals, Bill Bidwill, claims that the average attendance at games is under 8,000, and he is therefore justified in moving the team to a city with a cheaper stadium.Identify the null hypothesis H0 and the alternative hypothesis H1. Use μ for a claim about a mean, p for a claim about a proportion, and σ for a claim about variation.




15.Agent Mulder's boss claims that the proportion of Americans that have seen a UFO, p, is less than 5 in every one thousand and thus the X-files should be closed forever. Identify the type II error for the test.

16.An importer of Cuban cigars claims that the percentage of genuine Cuban tobacco in each Churchill is at least 80%. Identify the type I error for the test.





17.The Maine Department of Natural Resources reported that the mean weight of lobsters trapped in the state is 1.7 pounds. Shelly is a lobster trapper off the coast of Maine. She suspects that this figure is too high so she records the weights of a random sample of 45 lobsters that she trapped. If x = 1.5 pounds and s = 0.6 pounds, use a 1 percent level of significance to test the state's figure of 1.7 pounds.

Originally Posted by wintergirl

Use the given degree of confidence and sample data to find the margin of error in estimating the population mean μ for the following scenario. College students' annual earnings: 99% confidence; n = 67, = $6068, s = $1000.




9.Find the margin of error for a sample of 12, where the mean is 61.4 and the standard deviation is 6.9. Use a 95% confidence interval.




10.The amounts (in ounces) of juice in eight randomly selected juice bottles are:

15.8 15.9 15.9 15.6 15.2 15.7 15.8 15.6

Construct a 98 percent confidence interval for the mean amount of juice in all such bottles.




11.The weekly earnings of students in one age group are normally distributed with a standard deviation of 100 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 5 dollars.

12.Smokey wishes to estimate the true proportion of all drivers who exceed the speed limit on a certain stretch of road where accidents frequently happen. How large should the sample be so that, with 93 percent confidence, the sample proportion will not differ from the true proportion by more than 0.01?




13.An estimate of the population proportion from a study on the incidence of hepatitis A in a certain time period is 0.25. In a new study, the researchers want a margin of error of 0.005 with 99% confidence level. Find the minimum sample size you should use to assure that your estimate, , will be within the required margin of error around the population p.




14.The owner of the Arizona Cardinals, Bill Bidwill, claims that the average attendance at games is under 8,000, and he is therefore justified in moving the team to a city with a cheaper stadium.Identify the null hypothesis H0 and the alternative hypothesis H1. Use μ for a claim about a mean, p for a claim about a proportion, and σ for a claim about variation.




15.Agent Mulder's boss claims that the proportion of Americans that have seen a UFO, p, is less than 5 in every one thousand and thus the X-files should be closed forever. Identify the type II error for the test.

16.An importer of Cuban cigars claims that the percentage of genuine Cuban tobacco in each Churchill is at least 80%. Identify the type I error for the test.





17.The Maine Department of Natural Resources reported that the mean weight of lobsters trapped in the state is 1.7 pounds. Shelly is a lobster trapper off the coast of Maine. She suspects that this figure is too high so she records the weights of a random sample of 45 lobsters that she trapped. If x = 1.5 pounds and s = 0.6 pounds, use a 1 percent level of significance to test the state's figure of 1.7 pounds.

It would be best if you showed the working you've done on each of these questions and where you get stuck.

Going to your class notes or textbook and familiarising yourself with the key formulae and concepts, as well as looking at worked examples, will help you a lot.