Women athletes at the a certain university have a long-termgraduation rate of 67%. Over the past several years, a randomsample of 40 women athletes at the school showed that 22 eventuallygraduated. Does this indicate that the population proportion ofwomen athletes who graduate from the university is now less than67%? Use a 1% level of significance.

(a) State the null and alternate hypotheses. H0: p < 0.67;H1: p = 0.67 H0: p = 0.67; H1: p < 0.67 H0: p = 0.67; H1: p ≠0.67 H0: p = 0.67; H1: p > 0.67

(b) What sampling distribution will you use? The standardnormal, since np < 5 and nq < 5. The standard normal, sincenp > 5 and nq > 5. The Student's t, since np > 5 and nq> 5. The Student's t, since np < 5 and nq < 5. What is thevalue of the sample test statistic? (Round your answer to twodecimal places.)

(c) Find the P-value of the test statistic. (Round your answerto four decimal places.) and Sketch the sampling distribution andshow the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you rejector fail to reject the null hypothesis? Are the data statisticallysignificant at level α? At the α = 0.01 level, we reject the nullhypothesis and conclude the data are statistically significant. Atthe α = 0.01 level, we reject the null hypothesis and conclude thedata are not statistically significant. At the α = 0.01 level, wefail to reject the null hypothesis and conclude the data arestatistically significant. At the α = 0.01 level, we fail to rejectthe null hypothesis and conclude the data are not statisticallysignificant.

(e) Interpret your conclusion in the context of the application.There is sufficient evidence at the 0.01 level to conclude that thetrue proportion of women athletes who graduate is less than 0.67.There is insufficient evidence at the 0.01 level to conclude thatthe true proportion of women athletes who graduate is less than0.67.