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 61 people who recently served as jurors. The sample mean wait time was six hours with a sample standard deviation of three hours. Construct a 95% confidence interval for the population mean time wasted. Round to 1 decimal place.

a. (4.8, 7.3)

b. (5.2, 6.8)

c. (5.0,7.0)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 6 hours

sample standard deviation = s = 3 hours

sample size = n = 61

Degrees of freedom = df = n - 1 = 61 - 1 = 60

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,60 = 2.000

Margin of error = E = t/2,df * (s /n)

= 2.000 * (3 / 61)

Margin of error = E = 0.8

The 95% confidence interval estimate of the population mean is,

  ± E  

= 6.0  ± 0.8

= ( 5.2, 6.8 )

correct option is = b