Question

9) In 2013, the mayor of a certain city began a mayor's court designed to hear cases involving traffic citations and misdemeanor charges. The purpose was to address the case backlog and to add to the city's revenue. During the first quarter of 2013, the mean fine was $64.98. Later in the year, a random sample of 15 fines from the mayor's court was obtained. The summary statistics were

x = 70.48

and

s = 15.57.

Is there any evidence to suggest that the mean fine has increased? Assume the underlying distribution is normal and use

α = 0.01.

a)Give the value of the appropriate t_{α, n − 1} or t_{α/2, n − 1}. (Round your answer to four decimal places.)

b)Calculate the test statistic. (Round your answer to four decimal places.)

t =

Answer 1

a)

H0: <= 64.98 ,

Ha: > 64.98

This is one tailed test.

For sample standard deviation, we use t test.

n-1 = 15 -1 = 14

t,n-1  = 2.6245

b)

Test statistics

t = ( - ) / (S / sqrt(n) )

= (70.48 - 64.98 ) / ( 15.57 / sqrt(15) )

= 1.3681

Since test statistics < 2.6245, do not reject H0.