Question

Do drivers of large trucks drive too many hours in a day? Officials believe that more than 15% of drivers log too many hours daily. At one truck inspection station they issued citations to 49 of 348 truckers that they reviewed.

Test an appropriate hypothesis. Be sure to include the following:

1. State the null and alternative hypotheses in symbols and words. Assume conditions have been met. (2 pts.)
2. Perform your hypothesis test "by hand" using the equation editor. Be sure to use the appropriate probability notation. (4 pts.)
3. Construct a 90% confidence interval, again showing calculations "by hand" (4 pts.)
4. State your conclusion making sure to site whether we reject or fail to reject and what that means in context. Then support your conclusion with the results from your confidence interval. Be sure to note whether the hypothesized value falls in our interval and what that means. (3 pts.)

Answer 1

Hypothesized Proportion of drivers who log too many hours daily : p_o= 15/100 = 0.15

p : Proportion of of drivers log too many hours daily

Null hypothesis : H_o : p = 0.15

Alternate hypothesis : H_a : p > 0.15

Number of drivers reviewed : Sample size : n= 348

Number of drivers issued citations of 348 truckers that were reviewed = 49

Sample Proportion of drivers who log too many hours daily : = 49/348=0.1408

Level of significance : = 0.10

For right tailed test:

As p-value : 0.6846 > Level of significance : 0.10 ; Fail to reject null hypothesis.

Formula for confidence interval for single population proportions : p

Confidence Level	90%
(= 100-90/100=10/100 ) = 0.1	0.1
/2 (=0.1/2=0.05)	0.05
	1.6449

90% Confidence Interval for Proportion of of drivers log too many hours daily

90% Confidence Interval for Proportion of of drivers log too many hours daily = 0.1101, 0.1705

as 0.15: the hypothesized value ; falls in our interval:( 0.1101, 0.1705) ; Fail Reject null hypothesis.