Question

1. A recent industry report indicated that 60% of drivers involved in a residential accident will be in at least one other traffic accident in the last 3 years. An advisory group decided to investigate this claim, believing it was too large. A sample of 400 traffic accidents this year showed 200 persons were also involved in another accident with in the last 3 years. Use the 0.10 significance level.
   1. Why can we use z as the test statistic?
   2. State the null and alternate hypothesis
   3. Show the decision rule graphically.
   4. Compute the value of z and state your decision regarding the null hypothesis.
   5. Determine and interpret the p value

Answer 1

Answer:

Given,

p^ = x/n = 200/400 = 0.5

Here we use z test

Ho : advising group decided to investigate that believing it was not too large

Ha : advising group decided to investigate that believing it was too large

test statistic z = (p^ - p)/sqrt(p(1-p)/n)

substitute values

= (0.5 - 0.6)/sqrt(0.6(1-0.6)/400)

= - 4.08

P value = 0.000045 [since from z table]

= 0.0000

Here p value < alpha,so we reject Ho.

So there is sufficient evidence to support the claim.