Question

The government introduced new laws requiring long distance truck drivers to take minimum rest breaks. Prior to introducing the new laws, the true proportion of long distance truck drivers who often felt tired while driving was 70%. A statistics student wanted to test whether the proportion of long distance truck drivers who often feel tired while driving had been reduced (below 70%) 6 months after the introduction the new laws. The student calculated the Z-test statistic based on a sample and found it was -2.25. What is the p-value for this test?

	a.	0.9878
	b.	0.0122
	c.	0.0244
	d.	0.4989

Answer 1

Let the proportion of truck drivers who felt tired=p

Its a one tail test.

Calculated value of Z=-2.25

We can refer to standard normal distribution tables. and find area under curve between Z=0 and Z=-2.25

Since standard normal distribution curve is symmetric about 0, area under curve between Z=0 and Z=2.25 is same as area between Z=0 and Z=2.25.

We get area under the curve (between Z=0 and Z=2.25) =0.4878

So, p=0.50-0.4878=0.0122

Correct option is

b) 0.0122