We want to test the claim that less than 15% of people have gotten a speeding ticket in the last yea

1

• We want to test the claim that less than 15 of
  people have gotten a speeding ticket in the last
  year. We sample 400 people, and 13 of our
  sample has gotten a speeding ticket.

This is a left-tailed test Lets use a0.05 (5
significance level)
2

• Test Statistic

Is this z-value unusual (unlikely to occur by
chance alone)? Traditional Method The bottom 5
of possibilities occur at z-values less than
-1.645 Since our test statistic does not fall
below -1.645, our test statistic is not unusual
(at the 5 significance level)
3
Traditional Method The bottom 5 of
possibilities occur at z-values less than
-1.645 Since our test statistic does not fall
below -1.645 (in the critical region), our test
statistic is not unusual (at the 5 significance
level)
4
P-Value Method What is the probability of
getting a z-value less than -1.12? P(zlt-1.12)
0.1314 So a z-value less than -1.12 would occur
in 13 of samples, even if p 0.15. This is not
unusual (doesnt occur less than 5 of the time,
based on our significance level).
5
Conclusion There is not sufficient sample
evidence to support the claim that less than 15
of people have gotten a speeding ticket in the
last year. This doesnt mean that were wrong,
just that either the true proportion is not very
much less than 15, or that our sample size was
not large enough to provide enough evidence.