7. A simple random sample of 25 highway speeds along a certain stretch of Hwy 1
ID: 3358943 • Letter: 7
Question
7. A simple random sample of 25 highway speeds along a certain stretch of Hwy 1 at a particular time of day has a mean of 60.2 mph and a deviations of all such speeds is normally distributed. a) What is the best point estimate of the standard deviation of the speeds of all motor vehicles on this stretch of Hwy 1 at this particular time of day? 2 pts) b) Find a 95% confidence interval estimate of the standard deviation of the speeds ofall motor vehicles on this stretch of Hwy 1 at this particular time of day. 4 pts) c) A public safety official has a theory that more traffic accidents occur when the standard deviation of the speeds of motor vehicles on the highway is larger than 6.8 mph. Does your confidence interval support the claim that the standard deviation of speeds along this stretch of Hwy 1 at this particular time of day is greater than 6.8 mph? Why or why not? (2 pts) 8. Find the P-value for a test statistic of -82.32 if n-51 and we are testing the claim that > 14.3 cm. Round to 4 decimal places. (4 pts)Explanation / Answer
Q7.
a.
point estimate of the standard deviation = 9.5
b.
ci = (n-1) s^2 / ^2 right < ^2 < (n-1) s^2 / ^2 left
where,
s = standard deviation
^2 right = (1 - confidence level)/2
^2 left = 1 - ^2 right
n = sample size
since alpha =0.05
^2 right = (1 - confidence level)/2 = (1 - 0.95)/2 = 0.05/2 = 0.025
^2 left = 1 - ^2 right = 1 - 0.025 = 0.975
the two critical values ^2 left, ^2 right at 24 df are 39.3641 , 12.401
s.d( s )=9.5
sample size(n)=25
confidence interval for ^2= [ 24 * 90.25/39.3641 < ^2 < 24 * 90.25/12.401 ]
= [ 2166/39.3641 < ^2 < 2166/12.4012 ]
[ 55.0248 < ^2 < 174.6605 ]
and confidence interval for = sqrt(lower) < < sqrt(upper)
= [ sqrt (55.0248) < < sqrt(174.6605), ]
= [ 7.4179 < < 13.2159 ]
c.
yes, it is as 6.5 is not lie in the confidence computed
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