Question 1171917: Please help me. This is a hypothesis testing problem. Professor Jennings claims that only 36% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 86 students shows that 33 have jobs. Do the data indicate that less than 36% of the students have jobs? Use ∝ = 0.05.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: p >=0.36
Ha: p < 0.36
alpha=0.05 p{reject Ho|Ho true}
One way test.
critical value is z < -1.645
z=(phat-p)/sqrt(p(1-p)/n)
33/86=0.384
Right there, the evidence is sufficient not to reject Ho, since the sample proportion is greater than 36%.
z=(0.384-0.36)/sqrt(0.36*0.64/86)
=0.46
This is obviously greater than -1.645 so fail to reject Ho
p-value =0.65
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Note, if it is to be proven that MORE than 36% have jobs (some implication by how the question was asked, that there was concern there were more than 36% working, not fewer), then Ho is p < =0.36 and Ha:p >0.36
and the critical value is z > 1.645.
Still fail to reject in this instance, in that the proportion of 38.4% of students working is within the margin of error with z not >1.645 and p-value 0.32.
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