SOLUTION: A recent study at a local college claimed that the proportion, p , of students who commute more than fifteen miles to school is no more than 25% . If a random sample of 255 student

Question 1147800: A recent study at a local college claimed that the proportion, p , of students who commute more than fifteen miles to school is no more than 25% . If a random sample of 255 students at this college is selected, and it is found that 78 commute more than fifteen miles to school, can we reject the college's claim at the 0.05 level of significance?
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.
g) The null hypothesis:
h) The alternative hypothesis:
i) The type of test statistic (Z, t, chi square, or f):
j) The Value of the test statistic (round to at least 3 decimal places):
k) The p-value (round to at least 3 decimal places):
l) Can we reject the claim that the proportion of students who commute more than fifteen miles to school is no more than YES OR NO?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho : p <=0.25
Ha: p > 0.25
p hat is 78/255=0.30588
alpha is 0.05, P{reject Ho|Ho true}, reject if P>1.645
test stat is a z (phat-p)/sqrt(p*(1-p)/n)
z=0.05588/sqrt(0.25*0.75/255)
z=2.06
reject Ho YES
p-value is 0.020
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