Question 1120541: MTV states that 75% of all college students have seen at least one episode of their TV show "Jersey Shore". Last month, a random sample of 120 college students was selected and asked if they has seen at least one episode of the show. Out of the 120, 85 of them said they had seen at least one episode. Is there enough evidence to claim the population proportion of all college student that have watched at least one episode is less than 75% at the 0.05 level of significance?
A) Are the requirements met to run a test like this?
B) What are the hypotheses for this test?
C) Compute the test statistic and the p-value for this test.
D) What is your conclusion at the 0.05 level of significance?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Yes,random sample with population defined as a one sample proportion test
Ho: p is >=0.75
Ha: p is < 0.75
alpha is 0.05 P{reject Ho|Ho true}
test stat is z=(p hat-p)/sqrt (p*(1-p)/n); p hat is 85/120, the point estimate, or 0.708
Critical value z<-1.645 one tail test
z=(0.708-0.75)/sqrt (0.75*0.25/120); sqrt term is 0.0395
=-0.042/ 0.0395
=-1.05
Fail to reject, p-value 0.15. Insufficient evidence to say that the true proportion is less than 0.75.
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