**Interpreting a Confidence Interval for a Population Mean**A student was asked to find a 95% confidence interval for a widget width using data from a random sample of size n = 15. Which of the following is a correct interpretation of the interval 10.1 < μ < 31.9?Check all that are correct.- [ ] With 95% confidence, the mean width of a randomly selected widget will be between 10.1 and 31.9.- [ ] The mean width of all widgets is between 10.1 and 31.9, 95% of the time. We know this is true because the mean of our sample is between 10.1 and 31.9.- [ ] With 95% confidence, the mean width of all widgets is between 10.1 and 31.9.- [x] There is a 95% chance that the mean of the population is between 10.1 and 31.9.- [ ] There is a 95% chance that the mean of a sample of 15 widgets will be between 10.1 and 31.9.

Answered: Interpreting a Confidence Interval for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A student was asked to find a 98% confidence interval for widget width using data from a random sample of size n = 22. Which of the following is a correct interpretation of the interval 13.7 < μ < 27.5? Check all that are correct. The mean width of all widgets is between 13.7 and 27.5, 98% of the time. We know this is true because the mean of our sample is between 13.7 and 27.5. There is a 98% chance that the mean of a sample of 22 widgets will be between 13.7 and 27.5. There is a 98% chance that the mean of the population is between 13.7 and 27.5. With 98% confidence, the mean width of a randomly selected widget will be between 13.7 and 27.5. With 98% confidence, the mean width of all widgets is between 13.7 and 27.5.
Wheaties cereal is claimed to have an average of 3 grams of dietary fiber per serving. We want to test this hypothesis and to see whether we believe that is true or that the mean amount of fiber is significantly different from 3 grams. A random sample of 25 servings was taken and it yielded a sample mean of 3.4 grams with the sample standard deviation in the amount of fiber, s = .8 grams. %3D Assume that software has determined the p-value to be.02. Carry out the test at the 5% level of significance. Be sure to state your decision rule and your decision for the test. O Fail to Reject the null hypothesis since the p-value is .05 O Fail to Reject the null hypothesis since the p-value is > .05
The mayor is interested in finding a 90% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 212 residents whose mean number of pounds of trash generated per person per week was 37.9 pounds and the standard deviation was 7.7 pounds. Round answers to 3 decimal places where possible. b. With 90% confidence the population mean number of pounds per person per week is between _______ and ________ pounds. c. If many groups of 212 randomly selected members are studied, then a different confidence interval would be produced from each group. About __________ percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about ____________ percent will not contain the true population mean number of pounds of trash generated per person per week.
A student was asked to find a 90% confidence interval for widget width using data from a random sample of size n = 20. Which of the following is a correct interpretation of the interval 12.6 < µ< 27.8? Check all that are correct. The mean width of all widgets is between 12.6 and 27.8, 90% of the time. We know this is true because the mean of our sample is between 12.6 and 27.8. There is a 90% chance that the mean of a sample of 20 widgets will be between 12.6 and 27.8. With 90% confidence, the mean width of all widgets is between 12.6 and 27.8. There is a 90% chance that the mean of the population is between 12.6 and 27.8. With 90% confidence, the mean width of a randomly selected widget will be between 12.6 and 27.8.
A student was asked to find a 90% confidence interval for widget width using data from a random sample of size n = 20. Which of the following is a correct interpretation of the interval (11.5,21.6)? There is a 90% chance that the mean of a sample of 20 widgets will be between 11.5 and 21.6. The mean width of all widgets is between 11.5 and 21.6, 90% of the time. We know this is true because the mean of our sample is between 11.5 and 21.6. With 90% confidence, the mean width of a randomly selected widget will be between 11.5 and 21.6. We are 90% confident the mean width of all widgets is between 11.5 and 21.6. There is a 90% chance that the mean of the population is between 11.5 and 21.6.
A student was asked to find a 98% confidence interval for widget width using data from a random sample of size n = 26. Which of the following is a correct interpretation of the interval 13.5 < μ < 29.3? Check all that are correct. The mean width of all widgets is between 13.5 and 29.3, 98% of the time. We know this is true because the mean of our sample is between 13.5 and 29.3. With 98% confidence, the mean width of a randomly selected widget will be between 13.5 and 29.3. There is a 98% chance that the mean of a sample of 26 widgets will be between 13.5 and 29.3. There is a 98% chance that the mean of the population is between 13.5 and 29.3. With 98% confidence, the mean width of all widgets is between 13.5 and 29.3.
Thunderstorm Speeds A meteorologist who sampled 10 thunderstorms found that the average speed at which they traveled across a certain state was 12 miles per hour. The standard deviation of the sample was 2.2 miles per hour. Use a graphing calculator and round the answers to at least one decimal place. Part 1 of 2 Find the 85% confidence interval of the mean. Assume the variable is normally distributed. 10.9 < u < 13.1 Part: 1/ 2 Part 2 of 2 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? The meteorologist should use miles per hour for the prediction.
Two confidence intervals, (119.4 Hz, 120.6 Hz) and (119.1 Hz, 120.9 Hz), are constructed for the mean resonance frequency (in Hz) for all tennis rackets of a certain type using the same sample data. Which interval represents the higher level of confidence? 9.
andomly selected students participated in an experiment to test their ability Co determine when one minute (60 seconds) has passed. Forty students yielded a a sample mean of 56.3 seconds. Assume that o = 6.5 seconds. %3D dents. Is it likely that their mean have an estimate that is reasonably close to 58 seconds?
A random sample of 55 airline pilots had an average yearly income of $99,000 with a standard deviation of $15,000. If we want to determine a 95% confidence interval for the average yearly income, what is the value of t? Develop a 95% confidence interval for the average yearly income of all pilots.
A8 Q3

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