SOLUTION: A statistics instructor at CCD claims that 70% of students use the contents from their Introduction to Statistics course in their future careers. You have some doubts about this cl

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Question 1159077: A statistics instructor at CCD claims that 70% of students use the contents from their Introduction to Statistics course in their future careers. You have some doubts about this claim and conduct a study of your own. You randomly survey 225 CCD graduates who took Introduction to Statistics and 160 say they have used content from their statistics course in their career.
At an α=0.10 level of significance, is there enough evidence to claim the proportion of students that will use statistics content in their career is different from 70%?
Write the appropriate hypothesis.
Perform the test using either the critical value method or the p-value method.
State the conclusion of the test and interpret it.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Ho: the proportion is 0.70
Ha: it is not 0.70. The wording does not give any hint as to whether you think it is greater than or less than 0.70
alpha=0.10 p{reject Ho|Ho true}
test stat is a z
reject if |z|>1.645
test is a 1 sample proportion
p hat is 0.711
z=(phat -p)/sqrt(p*(1-p)/n)
=0.011/sqrt(0.71*0.29/225) sqrt term=0.0303
z=0.36
fail to reject Ho. There is insufficient evidence to reject the claim that the true proportion is 70%
p-value is 0.72