Question

1. A new program in Kentucky is designed to reduce the proportion of gas tank leaks at service stations.  Prior to the program, it was estimated that as many as 30% of gas tanks at Kentucky services stations had leaks.  They want to demonstrate that the program was effective.  After implementation, the state took a random sample of n = 40 service stations, and found that only 9 had leaks ( = 0.225). All conditions for this hypothesis test are met.

1. 1. Write the null and alternate hypothesis for this test.

Answer 1

Ans:

Test statistic:

z=(0.225-0.3)/SQRT(0.3*(1-0.3)/40)

z=-1.035

p-value=P(z<-1.035)=0.1503

Fail to reject the null hypothesis.

There is not sufficient evidence to conclude that the program was effective.