7 of 8 ID: MST.CI.CIM.04.0010b [4 points The Police Department is investigating

Question

7 of 8 ID: MST.CI.CIM.04.0010b [4 points The Police Department is investigating the need for a speed camera to be implemented on Swift Road. A sample of 51 cars passing through that road on a particular day were randomly selected and their speeds recorded. The speed limit on Swift Road is 60 miles per hour (mph). The mean speed for the sample was calculated as 43 mph. The standard deviation of the speeds for the sample was calculated as 5 mph. The standard deviation for the population of cars driving on Swift Road is unknown a) Select all the techniques that are commonly used to construct a confidence interval for the mean when the population standard deviation (a) is unknown Approximate the population standard deviation (?) with the sample standard deviation (s) D Replace the sample size (n) with n-1 D Approximate the standard normal distribution with the Student's t distribution 0 Decrease the confidence level to compensate for the increased margin of error b) Calculate the upper and lower bounds of the 99% confidence interval for the mean speed traveled on Swift Road Give your answers in mph to 2 decimal places. Upper bound mph Lower bound = mph

Explanation / Answer

Solution:

since population standard deviation is not known,use t distribution

OPTION C

Approximate the standard normal distribution with the student.s t distribution.

Solutionb:

n=sample size=51

df=n-1=51-1=50

sample mean=x bar=43

sample sd=5

alpha=1-0.99=0.01

0.01/2=0.005

t crit=2.6778

99% confidence interval for mean is

sample mean-t *samplesd/sqrt(n),sample mean+t *samplesd/sqrt(n)

43-2.6778*5/sqrt(51),43+2.6778*5/sqrt(51)

41.13,44.87

upper bound:44.87 mph

lower bound:41.13 mph

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