Women athletes at a certain university have a long -term graduation rate of 67%.

Question

Women athletes at a certain university have a long -term graduation rate of 67%. Over the past several years, a random sample of 42 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% of significance.

What is the value of the sample statistic? (Round to three decimal places)

Find the P-value of the test statistic. (Round your answer to four decimal places.)

Explanation / Answer

Set Up Hypothesis
Null, H0:P=0.67
Alternate,proportion of women athletes is less than 67% H1: P<0.67
Test Statistic
No. Of Success chances Observed (x)=23
Number of objects in a sample provided(n)=42
No. Of Success Rate ( P )= x/n = 0.5476
Success Probability ( Po )=0.67
Failure Probability ( Qo) = 0.33
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.54762-0.67/(Sqrt(0.2211)/42)
Zo =-1.6867
| Zo | =1.6867
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =1.687 & | Z | =2.33
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail -Ha : ( P < -1.68672 ) = 0.04583
Hence Value of P0.01 < 0.04583,Here We Do not Reject Ho

[ANSWER]

Zo =-1.6867, P-value : 0.04583

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