In need of help with Statistics Word Problems

Question

According to an article in Bloomberg Businessweek, New York City's most recent adult smoking rate is 14%. Suppose that a survey is conducted to determine this year's rate. Nine out of 70 randomly chosen N.Y.C residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still 14% or if it has decreased? Does the data support the claim at the 5% significance level?

Be sure to include your 1) Decision (reject or accept the null), 2) Reason for the decision and 3) Conclusion (write in a complete sentence) (Just like examples)

Answer 1

Step 1: State Ho and Ha

Ho: p=.14

Ha: p <> .14

Step 2: State 2 tail test and verify that it can be normal approximated.

np >= 5 and nq >=5

n=70 p^=9/70=.129 Level of error is .05

70(.14) = 9.8 >=5 check 70(.86) >= 5 60.2 >= 5 check

Step 3: Find critical values for z

zc = invnorm(.05/2) = -1.95 and zc = invnorm(1-.05/2) = 1.96

These would be your boundaries on the normal curve.

Step 4: Find the test statistic z*

z* = (p^-p)/ sqr(pq/n) = (.129-.14) / sqr(.14*.86/70) = -.27

Step 5: Reject or Do Not Reject Ho

z* is between -1.95 and 1.96 therefore we DO NOT reject Ho

Because z* is not in the rejection region. you decide to not reject the null hypothesis. In other words, there is not enough evidence to support the claim that the smoking rate has increased or decreased in any way.