George and Jerry are working on their final project for AP Statistics. They wish

Question

George and Jerry are working on their final project for AP Statistics. They wish to investigate the question, "Do people really read documents they are asked to sign?" They believe that fewer than half of all people read a document they have been asked to sign. To test their theory, they randomly select 50 individuals from various locations and then present them with various fake documents. After being presented with the documents, the individuals are asked to sign them. George and Jerry then observe whether or not the individuals read the document. Out of the 50 individuals they selected, 7 read the document then refuse to sign; 15 read it and sign; and the remaining 28 do not read the document, but sign it anyway. Does the sample result provide sufficient evidence to support George and Jerry's theory that fewer than half of all people actually read a document they have been asked to sign?

A. Carry out an appropriate test at a 5% level of significance to test George and Jerry's theory.

B. Interpret the P-Value you calculated in part A

C. Construct and interpret a 95% confidence interval for P.

Explanation / Answer

Set Up Hypothesis
Null, H0:P=0.5
Alternate, George and Jerry's theory fewer than half people read H1: P<0.5
Test Statistic
No. Of Success chances Observed (x)=22
Number of objects in a sample provided(n)=50
No. Of Success Rate ( P )= x/n = 0.44
Success Probability ( Po )=0.5
Failure Probability ( Qo) = 0.5
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.44-0.5/(Sqrt(0.25)/50)
Zo =-0.8485
| Zo | =0.8485
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =0.849 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail -Ha : ( P < -0.84853 ) = 0.19807
Hence Value of P0.05 < 0.19807,Here We Do not Reject Ho

We don't have evidence o support George and Jerry's theory

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