Female athletes at the University of Colorado, Boulder, have a long-term graduation rate of 67% (Source: Chronicle of Higher Education). Over the past several years, a random sample of 38 female athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of female athletes who graduate from the University of Colorado, Boulder, is now less than 67%? Use a 5% level of signicance.

Yes, we can assume that the percent of female athletes graduating from the University of Colorado is less than 67%.

Step-by-step explanation:

We need to find p-value first:

z statistic = (p⁻ - p0) / √[p0 x (1 - p0) / n]

p⁻ = X / n = 21 / 38 = 0.5526316

the alternate hypothesis states that p-value must be under the normal curve, i. e. the percent of female athletes graduating remains at 67%

H1: p < 0.67

z = (0.5526316 - 0.67) / √[0.67 x (1 - 0.67) / 38] = - 0.1173684 / 0.076278575

z = - 1.538681

using a p-value calculator for z = - 1.538681, confidence level of 5%

p-value =.062024, not significant

Since p-value is not significant, we must reject the alternate hypothesis and retain the null hypothesis.