Question

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 14% of the 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.

Answer 1

(0.109 ; 0.171)

Explanation:

Phat ± Zcritical * sqrt[(phat(1 - phat)) / n]

Phat = 0.14 ; n = 348

1 - phat = 1 - 0.14 = 0.86

Zcritical at95% = 1.96

0.14 ± 1.96*sqrt[(0.14(0.86)) / 348]

0.14 ± 0.0308117

Lower boundary (0.14 - 0.0308117) =

Upper boundary = (0.14 + 0.0308117)

Hence, interpreting the meaning of 95% confidence interval ; this means that there is 95% confidence that the average proportion of trucks that have driven too may hours lies within the interval above.