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2 weeks ago
Truckers On many highways state police officers conduct inspections of driving logbooks from large trucks to see if the trucker has driven too many hours in a day. At one truck inspection station they issued citations to 49 of 348 truckers that they reviewed.
a. Based on the results of this inspection station, construct and interpret a 95% confidence interval for the proportion of truck drivers that have driven too many hours in a day.

b. Explain the meaning of "95% confidence" in part A.
Textbook 

Stats: Modeling the World


Edition: 4th
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a.  Conditions:
* Independence: We assume that one trucker's driving times do not influence other trucker's driving times.
* Random Condition: We assume that trucks are stopped at random.
* 10% Condition: This sample of 348 truckers is less than 10% of all truckers.
* Success/Failure: 49 tickets and 299 tickets are both at least 10, so our sample is large enough.
Under these conditions the sampling distribution of the proportion can be modeled by a Normal model. We will find a one-proportion z-interval.

We know n = 348 and = 0.14 , so SE() = = = 0.0186
The sampling model is Normal, for a 95% confidence interval the critical value is z* = 1.96.
The margin of error is ME = z* × SE() = 1.96(0.0186) = 0.0365.
The 95% confidence interval is 0.14 ± 0.0365 or (0.1035, 0.1765).
We are 95% confident that between 10.4% and 17.7% of truck drivers have driven too many hours in a day.

b. If we repeated the sampling and created new confidence intervals many times we would expect about 95% of those intervals to contain the actual proportion of truck drivers that have driven too many hours in a day.
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