Chapter 9.3, Problem 10P

For Problems 7-21. please provide the following information.

(a) What is the level of significance? State the null and alternate hypotheses.

(b) Check Requirements What sampling distribution will you use? Do you think the sample size is sufficiently large? Explain. Compute the value of the sample test statistic and corresponding z value.

(c) Find the p-value of the lest statistic. 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 significant at level $\alpha$?

(e) Interpret your conclusion in the context of the application.

College Athletics: Graduation Rate Women 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 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.