Question

A simple random sample is conducted of 2000 college students, 1289 of them have student loans. Use 1% significance level to test the claim that most college students have student loans (over 50%).

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Answer 1

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We make use of the Z-table to get the cumulative probability.

Claim will be "accepted" or the null hypothesis is rejected if p-value is less than 1% level of sig.

p-value = P(p > .50)
pcap = x/n = 1289/2000 = 0.6445
p-value = P(Z> (pcap-p)/sqrt(p*p'/n))
= P(Z> (.6445-.50)/sqrt(.5*.5/2000))
= P(Z>12.924)
= 0.00 , which is less than .01 level of sig.

ANSWER:Hence, we reject Ho and conclude that the CLAIM IS CORRECT. Yes, most collage students have students loans