SOLUTION: Dear tutor, Can you please check if my answer are correct? Thank you in advance. Q. Suppose that a committee is studying whether or not there is waste of time in our judicial

Question 1003719: Dear tutor,
Can you please check if my answer are correct? Thank you in advance.
Q. 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 four hours.
a. Define the random variables X and X- in words.
-X is amount of time individuals waste at the courthouse waiting to be called for jury duty. X- is mean amount of time that sample of 81 people who recently served at jurors.
b.Which distribution should you use for this problem? Explain your choice.
- use student's t distribution because we do not know population standard deviation (not positive with this answer.)
c.Construct a 95% confidence interval for the population mean time wasted.
N=81 Sample Mean= 8 sample standard deviation =4
df=81-1=80
a=1-CL=1-0.95 =0.05 0.05/2=0.025 the area to the left of t0.025 is 1-0.025=0.0975 look it up on t table. value is 1.990
EMB=(1.990)(4/square root of 81) = 0.8845
Mean-0.8845=8-0.8845 =7.1155
Mean+0.8845=8+0.8845 = 8.8845
Answer: (7.1155, 8.8845)
d.Explain in a complete sentence what the confidence interval means.
-We estimate with 95 % confidence that population is between 7.1155 and 8.8845 (not positive with this sentence.)
Thank you for your help!
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
You use a t-test because you don't know the population sd and assume the sample sd is a valid estimate of it.
The CI is 1.99 *s/sqrt(n)=1.99*4/9=0.884, and everything else is fine.
The long form of the answer for a CI is we don't know what the true value is and we will never know, but we are highly confident (95%) that the interval we construct will contain that parameter.
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