Women Athletes at the UC Boulder have a longterm graduation

Women Athletes at the UC, Boulder, have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 17 eventually graduated. Calculate the 99% confidence interval for the graduation rate of women athlete at this university and interpret your interval.
CI = 0.242,0.658
What is the standard error and margin of error?
SE= 0.081          ME=0.208
Based on the confidence interval, can you conclude that the graduation rate is now higher than 67%? Justify.
With 99% confidence, the population proportion of women athletes who eventually graduated is between 0.242 and 0.658. Since 67% does not fall inside this interval, we do not have sufficient evidence that the graduation rate of women athletes is higher than 67%.

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Solution

Women Athletes at the UC, Boulder, have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 17 eventually graduated. Calculate the 99% confidence interval for the graduation rate of women athlete at this university and interpret your interval.
CI = 0.242,0.658
What is the standard error and margin of error?
SE= 0.081          ME=0.208
Based on the confidence interval, can you conclude that the graduation rate is now higher than 67%? Justify.
With 99% confidence, the population proportion of women athletes who eventually graduated is between 0.242 and 0.658. Since 67% does not fall inside this interval, we do not have sufficient evidence that the graduation rate of women athletes is higher than 67%.

Confidence Interval Estimate for the Proportion

Data

Sample Size

38

Number of Successes

17

Confidence Level

99%

Intermediate Calculations

Sample Proportion

0.447

Z Value

2.576

Standard Error of the Proportion

0.081

Interval Half Width

0.208

Confidence Interval

Interval Lower Limit

0.239

Interval Upper Limit

0.655

CI = ( 0.239, 0.655)

Based on the confidence interval, can you conclude that the graduation rate is now higher than 67%? Justify.
With 99% confidence, the population proportion of women athletes who eventually graduated is between 0.239 and 0.655. Since 67% does falls above this interval, we do not have sufficient evidence that the graduation rate of women athletes is higher than 67%.

Your answers are correct.