Question

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 seven hours with a sample standard deviation of four hours.

1. b) Define the random variables X and X (with line over it)  in words.

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 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 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.

2. Which distribution should you use for this problem? (Enter your answer in the form z or t_df where df is the degrees of freedom.)

Explain your choice.

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 standard normal distribution should be used because the sample standard deviation is known.The Student's t-distribution for 81 degrees of freedom should be used because the sample standard deviation is known

3. Explain in a complete sentence what the confidence interval means.

We are 95% confident that a 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.     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.

Answer 1

1. X can be defined as amount of time individuals waste at the courthouse waiting to be called for jury duty.

Explanation: As we are interested in finding the amount of time individuals waste at the courthouse waiting tobe called for jury duty which is a random quantity so in the given question is taken as our random variable of interest.

2.The Student's t-distribution for 80 degrees of freedom should be used because we do not know the population standard deviation.

Explanation: We know that when the population standard deviation is unknown quantity then we use ' t-statistic' with n-1 degree of freedom where n is the sample size. So here we don't have knowledge of population standard deviation and we are supposed to test the hypothesis for mean time to wait, we sampled 81 individuals so 81-1=80 is required degree of freedom and sample statistic is "t" and test is t test.

3.We are 95% confident that the true population mean wait time at the courthouse lies within this interval.

Explanation: Confidence interval is the type of estimation based on the observed data for the unknown value of population parameter say mean or variance. If x1, x2,.....,xn be set of sample values and confidence interval is y(gamma), then a valid confidence interval has probability y of containing the true popular parameter of interest which is in this case is mean.