Suppose that a committee is studying whether or not there is waste of time in ou
ID: 3062565 • Letter: S
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 7 hours with a sample standard deviation of 3.3 hours.
a) Which distribution should you use for this problem? 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 Student's t-distribution for 81 degrees of freedom should be used because the sample standard deviation is known.
-The standard normal distribution should be used because the sample standard deviation is known.
-The standard normal distribution should be used because the population standard deviation is known.
b) Construct a 95% confidence interval for the population mean time wasted.
c) 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.
-There is a 95% chance 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.
-We are 95% confident that the true population mean wait time at the courthouse lies within this interval.
Explanation / Answer
The statistical software output for this problem is:
One sample T summary confidence interval:
: Mean of population
95% confidence interval results:
Hence,
a) The Student's t-distribution for 80 degrees of freedom should be used because we do not know the population standard deviation. Option A is correct.
b) 95% confidence interval: (6.27, 7.73)
c) We are 95% confident that the true population mean wait time at the courthouse lies within this interval. Option D is correct.
Mean Sample Mean Std. Err. DF L. Limit U. Limit 7 0.36666667 80 6.2703101 7.7296899Related Questions
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