For the following question: State the null and alternative hypothesis. Select th

Question

For the following question:

State the null and alternative hypothesis.
Select the distribution to use.
Write the decision rule. (Define the rejection region.)                                                                                                                                                      Calculate the test statistic.
Calculate the p-value.
Make a decision.                                                                                                                                                                                                              (Additional step for this worksheet) State the type I and II error in context of the problem.

The percentage of physicians who are women is 27.9%. In a survey of physicians
employed by a large university health system, 45 of 120 randomly selected physicians
were women. Is there sufficient evidence at the 0.10 level of significance to conclude
that the proportion of women physicians at the university health system exceeds
27.9%?

Explanation / Answer

Z-Test For Proportion
Set Up Hypothesis
Null, H0:P<0.279
Alternate,women physicians at the university health system exceeds H1: P>0.279
Test Statistic
No. Of Success chances Observed (x)=45
Number of objects in a sample provided(n)=120
No. Of Success Rate ( P )= x/n = 0.375
Success Probability ( Po )=0.279
Failure Probability ( Qo) = 0.721
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.375-0.279/(Sqrt(0.201159)/120)
Zo =2.3447
| Zo | =2.3447
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =2.345 & | Z | =1.28
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 2.34473 ) = 0.00952
Hence Value of P0.1 > 0.00952,Here we Reject Ho

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