8. [44.08 Points] BBUNDERSTAT12 8.3.D10.MI.S. ASK YOUR TEACHER Women athletes at a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 36 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 is now less than 67%? Use a 10% level of signicance. USE S (a) What is the level of signicance? |:| (b) State the null and alternate hypothems. O HO: p 0.6? O Ho: p - 0.67,- H1: p 5 and rJq > 5. O The Student's t, since Hp 5 and no > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) |:| (c) Find the P-value of the best statistic. (Round your answer ho four decimal places.) |:| Sketch the sampling distribution and show the area corresponding to the P-value. (d) Based on your answers in parts (a) to {c}, will you reject or fail to reject the null hypothesis? Are the data statistically signicant at level a? C) At the a - 0.10 level, we reject the null hypothesis and conclude the data are statistically signicant. O At the u - 0.10 level, we reject the null hypothesis and conclude the data are not statistically signicant. 0 At the u - 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically signicant. 0 At the 11 - 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically signicant. (e) Interpret your conclusion in the context of the application. 0 There Is sufcient evidence at the 0.10 level to conclude that the true proportion of women athletes who graduate ls less than 0.67. Q There Is insufcient evidence at the 0.10 level to conclude that the true proportion of women athletes who graduate is less than 0.67