SOLUTION: One​ study, based on responses from 1,017 randomly selected​ teenagers, concluded that 41​% of teenagers cite grades as their greatest source of pressure. Use a 0

Algebra ->  Probability-and-statistics -> SOLUTION: One​ study, based on responses from 1,017 randomly selected​ teenagers, concluded that 41​% of teenagers cite grades as their greatest source of pressure. Use a 0      Log On


   

Question 1045260: One​ study, based on responses from 1,017 randomly selected​ teenagers, concluded that 41​% of teenagers cite grades as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of all teenagers in the population feel that grades are their greatest source of pressure.
What is the null and alternative hypotheses?
Find the test statistic.
z=? ​(Round to two decimal places as​ needed.)
Find the​ P-value for the found test statistic.
​P-value=? (Round to four decimal places as​ needed.)
State the conclusion. Choose the correct answer below.
A.Reject Upper H 0. There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
B.Reject Upper H 0. There is insufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
C.Do not reject Upper H 0. There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
D.Do not reject Upper H 0. There is insufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Ho: > or = to half of all teenagers feel grades are the greatest source of pressure.
Ha: < than half of all teenagers feel this way.
alpha is 0.05, one tail test.
Test statistic is a one sample proportion: z=(phat-0.5)/sqrt {(0.5)(0.5)/1017} phat-p=-0.09; SE=0.0157
Critical value is z=<-1.645
z=-5.74
Strongly reject Ho with p<<0.0001
There is sufficient evidence to reject the null hypothesis. A