Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of three hours. Part (a) (i) Enter an exact number as an integer, fraction, or decimal. x= hrs (ii) Enter an exact number as an integer, fraction, or decimal. Sx= hrs (iii) Enter an exact number as an integer, fraction, or decimal. n = (iv) Enter an exact number as an integer, fraction, or decimal. n-1= Part (b) (b) Define the random variables X and X in words. ○ X is the amount of time an individual waits at the courthouse to be called for service. X is the mean wait time for a sample of individuals. ○ X is the number of individuals at the courthouse to be called for service. X is the average number of individuals at the courthouse. ○ X is the amount of time an individual waits at the courthouse to be called for service. X is the mean wait time for a sample of individuals. ○ X is the number of individuals at the courthouse to be called for service. X is the average number of individuals at the courthouse. Part (c) Which distribution should you use for this problem? (Enter your answer in the form z or toff where df is the degrees of freedom.) Explain your choice. ○ The standard normal distribution should be used because the sample standard deviation is known. The Student's t-distribution for 80 degrees of freedom should be used because we do not know the population standard deviation. The standard normal distribution should be used because the population standard deviation is known. ○ The Student's t-distribution for 81 degrees of freedom should be used because the sample standard deviation is known. Part (d) Construct a 95% confidence interval for the population mean time wasted. (i) State the confidence interval. (Round your answers to two decimal places.) hrs (ii) Sketch the graph. (Round your answers to two decimal places. Enter your a/2 to three decimal places.) CL = (iii) Calculate the error bound. (Round your answer to two decimal places.) hrs NR ☑ Part (e) Explain in a complete sentence what the confidence interval means. There is a 95% chance that a wait time at the courthouse lies within this interval. ○ We are 95% confident that the true population mean wait time at the courthouse lies within this interval. ○ We are 95% confident that the mean wait time at the courthouse of the sample of 81 individuals waiting at the courthouse lies within this interval. ○ We are 95% confident that a wait time at the courthouse lies within this interval.

Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of three hours. Part (a) (i) Enter an exact number as an integer, fraction, or decimal. x= hrs (ii) Enter an exact number as an integer, fraction, or decimal. Sx= hrs (iii) Enter an exact number as an integer, fraction, or decimal. n = (iv) Enter an exact number as an integer, fraction, or decimal. n-1= Part (b) (b) Define the random variables X and X in words. ○ X is the amount of time an individual waits at the courthouse to be called for service. X is the mean wait time for a sample of individuals. ○ X is the number of individuals at the courthouse to be called for service. X is the average number of individuals at the courthouse. ○ X is the amount of time an individual waits at the courthouse to be called for service. X is the mean wait time for a sample of individuals. ○ X is the number of individuals at the courthouse to be called for service. X is the average number of individuals at the courthouse. Part (c) Which distribution should you use for this problem? (Enter your answer in the form z or toff where df is the degrees of freedom.) Explain your choice. ○ The standard normal distribution should be used because the sample standard deviation is known. The Student's t-distribution for 80 degrees of freedom should be used because we do not know the population standard deviation. The standard normal distribution should be used because the population standard deviation is known. ○ The Student's t-distribution for 81 degrees of freedom should be used because the sample standard deviation is known. Part (d) Construct a 95% confidence interval for the population mean time wasted. (i) State the confidence interval. (Round your answers to two decimal places.) hrs (ii) Sketch the graph. (Round your answers to two decimal places. Enter your a/2 to three decimal places.) CL = (iii) Calculate the error bound. (Round your answer to two decimal places.) hrs NR ☑ Part (e) Explain in a complete sentence what the confidence interval means. There is a 95% chance that a wait time at the courthouse lies within this interval. ○ We are 95% confident that the true population mean wait time at the courthouse lies within this interval. ○ We are 95% confident that the mean wait time at the courthouse of the sample of 81 individuals waiting at the courthouse lies within this interval. ○ We are 95% confident that a wait time at the courthouse lies within this interval.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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