Here's the information:
One-third of all ex-convicts return to jail within 3 years. One state is trying a new rehabilitation system fr its prisoners. After the release of 50 prisoners who had participated in the new system, only 13 returned within 3 years. the null and alternative hypotheses are: Ho: p = 1/3 vs. Ha: p ≠ 1/3.
Question 1:
To test the null hypothesis, the approximate observed value of the z-statistic is:
For this question I use the formula
z = (p̂ - p) / (sqrt[p(1-p)] / n)
z = (.26 - .33) / (sqrt[.33*.66)] / 50) = -1.06 < this is my answer (the key says it's -1.10)
Question 2:
What is the approximate p-value of the observed z-statistic?
I'm stuck here.
I think I need to use normcdf(-1.06, (9^9)), but using this I get .853 and the answer key says it's .27. What am I doing wrong here? I know it's two tailed because the alternative is ≠, but even if I multiply .853 by 2 I'm still not getting the correct answer.
Any and all help is appreciated. The one who explains it best and correctly gets the ten points. Thank you!!
One-third of all ex-convicts return to jail within 3 years. One state is trying a new rehabilitation system fr its prisoners. After the release of 50 prisoners who had participated in the new system, only 13 returned within 3 years. the null and alternative hypotheses are: Ho: p = 1/3 vs. Ha: p ≠ 1/3.
Question 1:
To test the null hypothesis, the approximate observed value of the z-statistic is:
For this question I use the formula
z = (p̂ - p) / (sqrt[p(1-p)] / n)
z = (.26 - .33) / (sqrt[.33*.66)] / 50) = -1.06 < this is my answer (the key says it's -1.10)
Question 2:
What is the approximate p-value of the observed z-statistic?
I'm stuck here.
I think I need to use normcdf(-1.06, (9^9)), but using this I get .853 and the answer key says it's .27. What am I doing wrong here? I know it's two tailed because the alternative is ≠, but even if I multiply .853 by 2 I'm still not getting the correct answer.
Any and all help is appreciated. The one who explains it best and correctly gets the ten points. Thank you!!
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The trouble is with your approximation of 1/3. Calculate as below.
z = (13/50 - 1/3) / (sqrt[1/3*2/3)] / 50)
The p-value (for z = -1.10) is 0.1357*2 = 0.2714
z = (13/50 - 1/3) / (sqrt[1/3*2/3)] / 50)
The p-value (for z = -1.10) is 0.1357*2 = 0.2714