Question

An engineer wishing to obtain the speed characteristics on a bypass around her city at a confidence level of 95%, and an acceptable limit of ± 1.0 mi/hr collected a total of 130 spot speed samples and determined that the variance is 25 (mi/hr)2. Has the engineer met with all of the requirements of the study?

Answer 1

Answer: N = 96.04

Explanation:

To check if the engineer has met with all required, let us calculate the number of spot speed observations by considering the number of spot speed observations, the standard deviation corresponding to the required confidence level, and d the limit of acceptance error in the average speed estimate.

Please find the attached file for the solution

Answer 2

Answer:

No

Explanation:

confidence level 95%

Z= 1.96

margin of error (d) = 1

variance = 25

S.D = $\sqrt{variance}$ = $\sqrt{25}$ = 5

To check if the minimum size requirements are met we apply

N = $\frac{Z*S.D}{d} = (\frac{1.96*5}{1} )$ = 96.04

The engineer did not meet all the requirements of the study since the 130 spot sample collected has a minimum sample size of 97