It has been claimed that at UCLA at least 40 of the students

It has been claimed that at U.C.L.A. at least 40% of the students live on campus. From 3 sample of 250 students, 90 live on campus. Does the evidence support this claim at alha = 0.01?

Solution

To test H0 : population proportion live at campus>= 0.40 ag. proportion < 0.40...

sample proportion = 90 / 250 =0.36
test statistics= ( 0.36 - 0.40 ) / sqrt [ 0.40* 0.60 / 250 ] = -1.290994...
p-value = 0.09835288...

p-value is > 0.01...

so, H0 is true..really at least 40% students live on campus!