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Women athletes at the university of colorado, boulder, have a long-term graduation rate of 67% (source: the chronicle of higher education). over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. does this indicate that the population proportion of women athletes who graduate from the university of colorado, boulder, is not less than 67%? use a 5% level of significance. find the p-value of the test statistic (round to the nearest ten thousandths).

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BlueSky06

 

The solution would be like this for this specific problem:

H0: p = p0, or 
H0: p ≥ p0, or 
H0: p ≤ p0 

 

find the test statistic z = (pHat - p0) / sqrt(p0 * (1-p0) / n) 

 

where pHat = X / n 

 

The p-value of the test is the area under the normal curve that is in agreement with the alternate hypothesis. 
H1: p ≠ p0; p-value is the area in the tails greater than |z| 
H1: p < p0; p-value is the area to the left of z 
H1: p > p0; p-value is the area to the right of z 

 

Hypothesis equation:

 

H0: p ≥ 0.67 vs. H1: p < 0.67 

 

The test statistic is: 
z = ( 0.5526316 - 0.67 ) / ( √ ( 0.67 * (1 - 0.67 ) / 38 ) 
z = -1.538681 

 

The p-value = P( Z < z ) 
= P( Z < -1.538681 ) 
= 0.0619

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