Question

2. An FM rock station claims that 90% of all its listeners are college students. A sponsor of the station decides to test this claim against the suspicion that the percentage is lower. A random sample of 1500 people is selected from the population of all listeners and it is determined that 1325 are college students. Perform a hypothesis test to answer the question: Do the sample results support the sponsor’s claim at α = 1 %?

State the hypotheses (in words & symbols):

H0:

Ha:

State the decision rule: ________________________________________________________

____________________________________________________________________________

sample result is: ____________________________________________________

State the Conclusion: ___________________________________________________

Can the sponsor reject the rock station's claim at α = 1%? EXPLAIN. (No credit will be given without an explanation.)______________________

___________________

Answer 1

H0: p = 0.90 ,

Ha: p < 0.90

Sample proportion $\hat{p}$ = 1325 / 1500 = 0.8833

Test statistics

z = $\hat{p}$ - p / sqrt(p(1-p) / n)

= 0.8833 - 0.90 / sqrt( 0.90 * 0.10 / 1500)

= -2.16

Decision rule= Reject H0 if z < 2.326

Since test statistics falls in non-rejection region, We fail to reject H0.

We conclude at 0.01 level that we fail to support the claim.