Section 93 7 Aggravated Assault In a random sample of 40 fel

Section 9.3

7. Aggravated Assault: In a random sample of 40 felons convicted of aggravated assault, it was determined that the mean length of sentencing was 54 months, with a standard deviation of 8 months. Construct and interpret a 95% condence interval for the mean length of sentence for an aggravated assault conviction. Source: Based on data from the U.S. Department of Justice.

Answer:

12. Theme Park Spending: In a random sample of 40 visitors to a certain theme park, it was determined that the mean amount of money spent per person at the park (including ticket price) was $93.43 per day with a standard deviation of $15. Construct and interpret a 99% condence interval for the mean amount spent daily per person at the theme park.

Answer:

Solution

7.

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    54          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    8          
n = sample size =    40          
              
Thus,              
              
Lower bound =    51.52081987          
Upper bound =    56.47918013          
              
Thus, the confidence interval is              
              
(   51.52081987   ,   56.47918013   )

****************

12.

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    93.43          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    15          
n = sample size =    40          
              
Thus,              
              
Lower bound =    87.3208844          
Upper bound =    99.5391156          
              
Thus, the confidence interval is              
              
(   87.3208844   ,   99.5391156   )