Due to traffic safety concerns, a police department wants to develop a 90% confi

Question

Due to traffic safety concerns, a police department wants to develop a 90% confidence interval to estimate the true average vehicle speed along a highway. 11 random vehicle speeds were measured, and the sample mean was found to be 55 m.p.h. (miles per hour). The population standard deviation is unknown, but the sample standard deviation was found to be 3 m.p.h. The distribution of traffic speeds is assumed to follow a normal distribution.

a. Compute the margin of error for the 90% confidence interval. Round your critical value to three decimal places. Do not round any other intermediate calculations. Round your final answer to three decimal places. Margin of error = m.p.h.

b. Using your answer to Part a, compute the 90% confidence interval for the true average traffic speed. Round your final answers to three decimal places. Lower confidence limit = m.p.h. Upper confidence limit = m.p.h.

c. Suppose a citizen claims that, on average, vehicles do not exceed the posted speed limit along this highway. If the posted speed limit is 55 m.p.h., is the citizen's claim contradicted? Yes. It is contradicted. No. It is not contradicted.

Explanation / Answer

Ans:

As,sample size,n<30 and population standard deviation is unknown,we will use t distribution.

Sample mean=55

sample standard deviation,s=3

n=11

df=11-1=10

critical t value=1.812

a)Margin of error=1.812*3/sqrt(11)=1.639

b)90% confidence interval

=55+/-1.639

=(53.361, 56.639)

c)As,Confidence interval include 55,so citizen's claim is contradicted.

Yes, It is contradicted.

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