New York State has recently changed its Regents exams to fol

New York State has recently changed its Regents exams to follow the Common Core curriculum. State officials want to know if the passing rate on the exams has changed since the switch. Under the old curriculum, 72% of students passed the Regents exam in geometry. Out of a random sample of 175 geometry Regents exams using the new Common Core, 107 of them had passing scores. Does this indicate that the population percentage of students passing the exam is different for Common Core than it used to be under the old curriculum?

1. The correct test to run in this situation is a

z-test for means.

t-test.

2-sample t-test.

1-proportion z-test.

2. The p-value for the correct test is

.001

.004

.006

.009

3. Using a 1% level of significance, the correct conclusion would be

reject H_O, the population percentage of passing scores on the new test is different than 72%

reject H_O, there is not enough evidence to say the population percentage of passing scores on the new test is different than 72%

fail to reject H_O, the population percentage of passing scores on the new test is different than 72%

fail to reject H_O, there is not enough evidence to say the population percentage of passing scores on the new test is different than 72%

4. The correct hypotheses for this test would be

H_o: p > .72

H_A: p = .72

H_o: p = .72

H_A: p > .72

H_o: p \"not =\" .72

H_A: p = .72

H_o: p = .72

H_A: p \"not =\" .72

Solution

(1)1-proportion z-test.

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(2) The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(107/175-0.72)/sqrt(0.72*(1-0.72)/175)

=-3.20

So the p-value= 2*P(Z<-3.20) =0.0014 (from standard normal table)

Answer: .001

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(3)reject H_O, the population percentage of passing scores on the new test is different than 72%

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(4)

H_o: p = .72

H_A: p \"not =\" .72