For both problems answer the following.
a) What is the level of significance? State null and alternate hypothesis.
b) What sampling distribution will you use? do you think the sampling size is sufficiently large? Explain, What is the value of the sample test statistics?
c) Find p-value of the test statistics,
d) Based on your answers in parts a & c, will you reject or fail to reject the null hypothesis? are the data statistically significance at level a?
e) State your conclusion in the context of the application.
1) College Athletics: Graduation Rate. Women Athletes at the University of Colorado 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 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university of Colorado Boulder is now less than 67%. Use a 5% level of significance.
2) Fishing Northern Pike. Athabasca Fishing Lodge is located on Lake Athabasca in northern Canada. In one of its recent brochures, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 64 out of a random sample of 83 guests did, in fact catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use = 0.05.
Detailed solution with explanation and equations.