Question

In some states, the law requires drivers to turn on their headlights when driving in the rain. A highway patrol office believes that less than one-quarter of all drivers follow this rule. As a test, he randomly samples 200 cars driving in the rain and counts the number whose headlights are turned on. He finds this number to be 41. Does the officer have enough evidence at the 10% significance lever to support his belief.

My question is, my instructor worked this problem out for us, he put the rejection region as -z.10=-1.645 and I believe that he is wrong and that it should be -1.282, am I correct?

Answer 1

Solution :

The null and alternative hypothesis is

H0 : p = 0.25

Ha : p < 0.25

= 0.10

This is the left tailed test,

P(z < z ) = 0.10

z < -1.282

yes is correct